I imagined the scenario for a story where the USSR still forms and will later fight in a Cold War with the USA. However, I am imagining a scenario where the tsar escapes, goes with some loyal followers to another location (on Asian continent or other location) and is able to establish a great power in the region, still being somewhat relevant on the global stage. Is there anyway for this scenario to realistically happen (tsar and members of his family escapes, form great power somewhere without it instantly being crushed by United States or USSR, etc.)?
If the Russian Empire in an alternate history has colonies in North America, such as Alaska and surrounding parts of Canada, the tsarist forces could retreat to Russian North America just like the Portuguese government retreated to Brazil when Napoleon invaded Portugal.
Here we would have a kind of cold war between USSR and RENA (Russian Empire of North America). The RENA would have massive propaganda efforts onto the mainland, trying to undermine the communist government's authority over the Russian people in any way possible. It would be a propoganda of conservative, traditional, orthodox values. Things would get interesting as that would force the communist government actually have positive changes in the mainland to legitimize their rule over the Russian people there. They would be forced by circumstances to make a better life for the people in order to prove that they are the more worthy rival government, instead of just acting without regard of the best interests of the people, knowing that any misstep would be used by the tsarist government as a propaganda opportunity. That would improve the quality of life of people in the USSR, and also preserve 19th century Russian culture in the RENA. The political history of the USSR would be completely different.
The RENA would also become a great power faster because they would get a lot of refugees from the mainland escaping the Soviets. Cossacks, Old Believers, merchants, peasants, scientists, engineers, philosophers, and any other people who fled the Soviet Union to United States, France, Germany, and elsewhere would most likely have instead gone to the RENA, boosting it's population. In particular scientists and engineers would have been a great benefit for that growing new country, allowing them to have at least an initial technological advantage over the Soviet Union.
A possibility would be of a five way cold war between USSR, RENA, USA, Nazi Germany, and Japanese Empire. Now with more players on the scene you no longer have a winner takes all scenario. Instead you have more healthy competition, and none of the individual players is strong enough to defeat the rest.
Escape execution - yes. Form an independent country - highly unlikely
From Nicolas II abdication on 2(15).03.1917 to his execution on 17.07.1918 there were multiple opportunities to spirit the former tsar away from his detention, especially early on. For example, in March-April 1917 there was an active plan to let Nicolas leave for England, however George V, after some hesitation, rejected the idea. At any rate, before Nicolas and his family were sent to exile in August 1917, a determined plan to let him escape the captivity had a very high chance of success.
A very good question is what to do next. In late 1917, Russian Monarchy had no base of power. There was no safe heaven for Nicolas II. He could reach England, and British authorities would be unlikely to deport him back, but former tsar would have no power there.
He could (at least formally) lead the White movement in Russian civil war. But then it is very unlikely that the two sides could fight to a standstill. White movement could prevail, and then there would be no Soviet Union, or it could be defeated, and then Nicolas would be another exiled monarch at best. There is just no middle ground - no natural defensible border in Russia where Bolsheviks and Tsarists reach some kind of balance. Retreating to distant areas like Far East, Caucasus or Crimea could only postpone the inevitable.
Getting out of St Petersburg in a hurry, as the masses are starting to revolt, you don't have many choices. At this point in history it's at least a week to get Asia. (I'd love to see them in China or Vietnam or something, but I just can't see them making the trek across Siberia).
They'd need somewhere really close, and if you're escaping by boat or road, there's a nearby state, about 100km away, which doesn't make it into the USSR.
Finland's independence is closely tied into the 1917 Russian revolution, the abdication of "Grand Prince of Finland" Tsar Nicholas the 2nd led to its independence.
After the February Revolution and the abdication of Tsar Nicholas II, Grand Prince of Finland, on 2 March (15 March N.S.) 1917, the personal union between Russia and Finland lost its legal base – at least according to the view in Helsinki. There were negotiations between the Russian Provisional Government and Finnish authorities.
I don't know what those negotiations were, but that could've been cover for "New Identity please". It's a short boat journey (~100km) from the Winter Palace in St Petersburg to Finland. Some dedicated loyalists could smuggle you out easily.
They've had a tricky relationship since. I can't see them forming a direct power, but they could form a secret government in exile, serviced by loyalists, waiting for the right moment to reveal themselves. Or they could rename themselves, disguise their policies, and run for government in the new country.
Forming your own Great Power is hard work, unless you're Giuseppe Garibaldi, and frankly if the Tsar could pull that off he probably wouldn't have lost his first Great Power. Far better to steal one... or perhaps salvage one.
Enter China. In 1916 the last Chinese Emperor died and the country descended into a mess of feuding warlords, all of them keen on gaining some advantage over their rivals. It wouldn't take much to convince one of the Nationalist warlords to take on an advisor who knew the vicious wiles of those fiendish revolutionaries... and as every evil vizier knows, the line between "warlord's trusted advisor" and "warlord" is razor-thin.
Now of course, the Nationalists eventually lost the fight for mainland China and fled to Taiwan, but it needn't have been so. If they had managed the fortunes of war better, they could have conceivably have come out on top, and by a very strange quirk of fate, Nicholas Romanov could've led a resurgent, capitalistic China into the world stage during the Cold War.
The real problem, as noted in the beginning, is explaining how a leader with the ruthless cunning and drive to see this campaign through, one who could beat Mao Zedong in a winner-take-all contest for China and steer his adopted country against his homeland, could've mismanaged his first realm so badly that it collapsed out from under him.
Maximum awryness: Rise of Siberian Russia
Actual historical context:
The Unsung Revolution of February which Took Place in March:
The Russian Empire entered willingly in the First World War, with all classes supporting what was perceived as an opportunity to strengthen the international prestige of the Rodina. Sadly, the Russian war effort did not prosper. The towering stupidity of the Russian high command, notably of the doomed General Samsonov and the clueless General Rennenkampf led to the disaster of the Second Battle of Tannenberg, where Russia lost almost 200,000 men against less than 15,000 German casualties. (The First Battle of Tannenberg happened half a millenium earlier; in that battle the Teutonic knights lost.) By 1915, the Russian forces were in full strategic retreat, losing Poland and Galicia, again with disproportionate casualties.
In the summer of 1915, Tsar Nicholas II assumed direct personal command of the army, leaving the governing of the empire in the hands of his loving wife, Alexandra, who at that time was besotted with the pseudo-mystical Grigori Rasputin, he whom Boney M famously called "Russia's greatest love machine".
By 1916, the situation went from terrible to horrible. On the front, the Brusilov Offensive advanced 60 kilometers in four months, at the cost of one million men. (As always, the Russians were experts at solving all military problems by using up expendable muzhiks.) On the home front, Rasputin was assassinated by a group of high noblemen led by Prince Yusupov; but the erratic leadership of Empress Alexandra devastated the economy, bringing Russia on the brink of famine; the most ingenious idea of conscripting the Muslim subjects of the empire to fight a deadly war in faraway Europe fired up the Basmachi insurrection.
Early 1917 did not see any improvement. "In the seventeen months of the 'Tsarina's rule', from September 1915 to February 1917, Russia had four Prime Ministers, five Ministers of the Interior, three Foreign Ministers, three War Ministers, three Ministers of Transport and four Ministers of Agriculture. This "ministerial leapfrog", as it came to be known, not only removed competent men from power, but also disorganized the work of government since no one remained long enough in office to master their responsibilities." (Orlando Figes, A People's Tragedy, 2008, quoted by Wikipedia.)
The people of Petrograd (= Sankt Peterburg, Saint Petersburg, the capital city of the Empire) had had enough. Sporadic strikes began on what the Russians called 18 February and everybody else called 3 March. By 10 March (25 February for the Russians, who were behind the times as usual), the city was in full revolt. The Duma, which was what passed for an Imperial Parliament, saw no way out but to issue a Manifesto requesting the Tsar to abolish absolute monarchy and grant a Constitution. Several Princes affixed their signature on the treasonous Manifesto.
On 16 March 1917, Nicholas II, Tsar of All the Russias, abdicated in favor of his brother, Grand Duke Michael, who promptly declined the crown. (This didn't save him. The Bolsheviks killed him one year later.) The country fell into the hands of the hastily assembled Provisional Goverment whose only vision was to run around like a headless chicken trying to find out What Was to Be Done.
Vladimir Ilyich "Lenin" Ulyanov, the greatest agent provocateur of all times:
Meanwhile, the Germans, exalted by what they perceived as the imminent collapse of Russia, decided to give it push. An officer of the German General Staff went to Switzerland and contacted Vladimir Ilyich Ulianov, aka Lenin, the head of the rabidly extremist Bolshevik faction of the Russian Social Democratic Labor Party and offered him transportation to Petrograd. Lenin jumped at the occasion, and arrived at Petrograd's Finland Station in April 2017.
In six short months, Lenin's inflamatory speeches and the violent tactics of his fanatical supporters destroyed Russia's political system, what was left of it, and rendered the Provisional Government powerless to run the country.
The Great October Socialist Revolution which Took Place in November:
On 23 October 1917 (10 October in Russia), the Central Committe of the Bolshevik Party adopted a resolution calling for immediate armed uprising. On 7 November (25 October in Russia), the Bolshevik Military-Revolutionary Committe of Petrograd lauched an armed uprising against the Kerensky Government. The Winter Palace, the main seat of the Russian Government, did not resist. (The 140 female soldiers of the Women's Battalion who were supposed to defend it did not feel like confronting 40,000 furious Bolsheviks.)
Initial points of departure:
The former Tsar is still at Tsarskoye Selo:
In real history, Alexander Kerensky, head of the Russian Directory (the interim government tasked with running the country while the Constituent Assembly assembled a Constitution for the newly proclaimed republic) escaped the Winter Palace and fled to Pskov, where he assembled an army an attempted to retake Petrograd.
In real history, the Imperial Family had been relocated to Tobolsk, east of the Urals, in Western Siberia. But in our changed timeline, the Tsar had refused to leave his residence at Tsarskoye Selo (= Imperial Village in English), and happily for him, Kerensky's troops did indeed manage to take Tsarskoye Selo.
The Junker Mutiny proves to be more efficient than in real history:
In real history, the mutiny of the cadets of the military schools in Petrograd was defeated before it began: one of the leaders of the mutiny managed to be arrested while carrying the plans for the uprising. In the new timeline, Aleksandr Arnoldovich Bruderer evades arrest, and the Junker Mutiny succeeds in its initial plan of seizing the telephone exchange and some key fortresses in Petrograd.
Kerensky's troops, with the Imperial Family, join with the Junker cadets and retreat in order to Pskov, where they make contact with the forces of General Nikolay Yudenich.
In real history, Yudenich fled to Finland, and did not return to the Russian Civil War until 1919. In the new timeline, Yudenich joins his meager force with the motley men of Kerensky, takes command and leads an organized retreat through Minsk to Kiev.
A slightly different Russian Civil War:
By December 1917, the situation in Russia is almost the same as in real history, with the difference that Yudenich, Kerensky and the Imperial Family are in Kiev, where they have a tenuous relationship with the Ukrainian Central Rada, which was hesitating between collaboration with the Bolsheviks and moving towards independence.
Seeing how the wind was blowing, Yudenich, Kerensky and the Imperial Family, protected by the Cadets and whetever Loyalist forces they had assembled, move South-East towards Rostov-on-Don, which was firmly held by the Volunteer Army led by Lavr Kornilov. The long retreat has finally come to an end, and the Imperial Family is safe.
Events follow now real history: Kornilov dies in his attempt to take Ekaterinodar; the Volunteer Army executes the fabled Ice March (this time with the official head of government and the Imperial Family in tow); Anton Denikin takes command of the White Forces in Southern Russia. The White Army launches the Kuban Offensive, taking control of South-Eastern Ukraine, Crimea, and the entire Kuban region between the Black Sea and the Caspian.
As in real history, the Bolsheviks sign the shameful Treaty of Brest-Litovsk, ignominiously exiting the First World War and leaving their allies (notably Romania, sob, sob) hanging in the wind.
Events continue along the real historical path (maybe with the presence of the Imperial Family leading to a less atrocious white terror in Denikin's area of control) until late 1918.
The decisive points of departure:
In real history, the Eastern and Western parts of the putative Russian Republic fighting against the Bolsheviks did not speak to one another, did not co-ordinate with one another and generally behaved as if the other part did not exist. Moreover, they had only the most tenuous relationship with the Allied intervention forces which were supposed to help them.
In the new timeline, Denikin, as soon as the Kuban offensive gave him control of the entire strip of land between the Black Sea and the Caspian north of the Caucasus, names Yudenich as head of the Co-ordination Service, and he establishes a joint planning committee aiming to harmonize the movements of the Western White Forces in South Russia with the mightier Eastern White Forces in Siberia.
As in real history, Leon Trotsky attempts to dupe Nestor Makhno's anarchist Black Army, which was wrecking havoc in Southern Ukraine, into attacking Denikin's forces in the rear; but this time Denikin is alert and obtains support from the Polish and Romanian intervention forces, which keep the anarchists occupied and take Odessa.
By judiciously timing its offensive to coincide with the great eastwards push of the Eastern White Forces, the Southern White Forces avoid defeat at Orel and succeed in establishing contact with Kolchak's forces in Samara and Ufa.
In the summer of 1919, the White Army holds a continuous piece of territory stretching from Crimea and Rostov-on-Don (on the northern shore of the Sea of Azov) through Tsaritsyn¹ (later named Stalingrad, now Volgograd) to Samara and Ufa and onwards to the entire Siberia. (The White forces really held Siberia through out the Civil War, and they really took Tsaritsyn, Samara and Ufa from time to time.)
Seeing that some sort of half-victory was at hand, Kolchack (or rather Kerensky, acting on behalf of Kolchack) manages to convince the the Supreme Allied Council to withdraw its insistence that Russia renounce forever the restoration of monarchy, with the intention to capitalise on the Russian muzhik's love for the Father Tsar.
The Supreme Allied Council reluctantly agrees to let a future Russian Constituent Assembly decide between republic and monarchy, and steps up the supply of materiel, both through the American-held Vladivostok and the Trans-Siberian railway, and through the much closer at hand Black Sea and Rostov-on-Don.
Helpfully, Mikhail Tukhachevsky is killed during his attempt to retake Ufa for the Bolsheviks in the autumn of 1919. With him, the Bolsheviks lose their only competent military commander.
In 1920, with their economy in tatters, with the approaching specter of famine profiling on the horizon, with their opponents enjoying a steady flow of weapons, ammunition and supplies, the Bolsheviks make overtures for peace. Trotsky and Bukharin lead the Soviet delegation, with the negotiations taking place in Tsaritsyn. The Whites agree to evacuate Crimea, giving the Reds access to the warm water port of Sevastopol; they keep Rostov-on-Don. The frontier is established from Roston-on-Don along the Don up to Kalach-na-Donu, then accross to the Volga at Tsaritsyn, up the Volga through Saratov and Samara, then east along the Kama to the confluence with the Belaya, along the Belaya to its source, then along the crest of the Ural Mountains to the Kara Sea. The Reds keep Novaya Zemlya, the Whites keep Vaygach Island.
In 1921, the Constituent Assembly of Siberian Russia, sitting in Yekaterinburg, proclaims the country a constitutional monarchy, with Nicholas II assuming the title of Emperor of Siberia and retaining considerable executive powers.
Basically, the Russian Empire splits into its European part and its Asiatic part. The Soviet Union retains 80% of the Empire's population and economy, while the new Empire of Siberia retains a lot of underpopulated territory, rich in minerals and timber.
The Russo/Chinese Border, but Probably Nowhere
The problem I see is not one of escape, there are plenty of dice rolls and coin flips during a revolution, and it wouldn't take much for the Tzar to have successfully bolted or one of the older children to escape. (I don't think a younger kid would have the gravitas you want, if just Anastasia escapes she's a figurehead sure, but unlikely to be a real ruler-in-exile imo.)
The tricky part is "Where do they go where they can still be a Power?" My first thought is somewhere in the Russian far east, where they might gather loyalist forces and form a new power base. Somewhere along the Sino/Russian border for instance. They go there, a less-immediately-vengeful Red Russia doesn't follow or makes a truce, and between Imperial Loyalists and encroaching into Chinese territory made easy pickings by the chinese civil war they could establish a decent manpower base. You could maybe get local (mongolian/chinese) support just by being a less-corrupt government than the warlords and providing local security. Though you would have to do some pretty slick deals with the Chinese nationalists and/or Communists to pull it off. So you can conceivably make them a Nation. Probably not a Great Power Worthy Nation however. Except that such a power, positioned to strike on behalf of the Nazis, could have war-changing implications. The Nazis were kept out of Moscow by troops transferred from the far east. Throw an actively hostile force in the far east and the USSR can't pull the men, Moscow falls, and maybe the USSR with it.
Of course the problem there is I don't see for an instant the Lenin or Stalin allowing part of Russia be independent of the USSR, especially with the Czar or his kin at its head.
If you want to keep all of Russia Soviet however I just don't see a place for them. The various chinese warlords/governments wouldn't take them in on their own when the russians could easily go after them. The western nations and colonies might take them in (I seem to recall talks about the Brits wanting to take the Czar and have him live in the Netherlands or somehwere) but that's a government-in-exile and not a real "Fielding an Army" Power for WWII. I guess you could always have the Czar/his kin escape in such a manner, then when the nazis take over strike some sort of deal. Hitler was a racist and a moron, but possessed a certain low cunning politically. Perhaps a malleable son or daughter of the Czar could have been used as a Slavic figurehead promised to be returned to the Russian people, and thereby foment internal problems for the USSR. The Czar was fairly well liked (though his wife was hated) and it might have helped the Axis cause, but that doesn't seem to be exactly what you're after.
As a world leader the Czar just wasn't liked enough, and didn't have the influence, to just vanish and set up as head of a new country somewhere else. King of england? Sure he might become head of South Africa or Canada or Australia in a pinch, but Czar of all the Russians? No. Not without some alt-history Russian overseas territories or a bit of handwavium anyway.
There is a novel by Vasily Aksenov called "The Island of Crimea" describing a scenario that may be useful for you. In that novel's world Crimea is an island, not a peninsula, and it gives refuge to the White movement after they lose the Civil War, with some aid from the British Navy. It becomes something akin to what Taiwan is to China. While in the novel Nicholas did not escape there, it certainly won't be impossible for that to happen.
Even though it won't be a Great Power comparable to USA/USSR, it could become quite wealthy and developed, and then, who knows, maybe snatch more land at the coast of the Black Sea, e.g. taking part in the partition of the Ottoman Empire.
And even if you don't want to alter the geography that much, altering history so there was a channel dug between Crimea and the mainland is reasonably plausible.