I Have Lived and Fought Alongside Uzbeks
I am a former Marine Infantryman and I have fought alongside the Uzbeks, albeit the ones in the northern alliance of Afghanistan where they are an ethnic minority. Uzbeks are....... odd. They live in a strange mixture of modernity and ancient custom. For instance you will find a man with an AK-47 and modern uniform who still believes that he and his brethren's military success is due to angels and good spirits, and has no qualms about riding a horse to get around or even in the attack. They tend to be very tenacious in the defense and highly skilled at ambushes, but once they have lost the initiative and element of surprise while on the attack they are a lot more likely to scatter and try the assault again later than stick it out and try to see it through. They also have this very frustrating habit of using the mantra "In'sh Allah." You could write a book detailing the various intricacies of what this means, but simply put it means "if God wills it." Need them to be on time and in position? "In'sh Allah" in other words "well, maybe we'll get to it, maybe we wont. God will decide." The western idea of "we will do everything possible in our power to get in position and be on time or die trying" just doesn't happen very often.
I say all of this because frankly, the Uzbeks simply couldn't conquer eastern Asia. Pakistan and Iran have far more professional and modern military mindsets than they do. The Uzbeks are mostly tribal and chiefdom oriented which is great for defending against incursions by pashto tribesmen and such (like they did against the Taliban back in 2001) but its really not great for offensive operations. The best they can really do is chase a harried enemy they defeated from the defensive a ways out of their territory. The last time the Taliban began moving in on the Uzbeks only american green berets and US lead airstrikes were able to chase the Taliban out of northern Afghanistan, and it was so close to becoming a defeat that at one point the Northern Alliance was literally one machine-gun crew failing to hold it's position away from utter defeat. The Pashto Afghan to the south vastly outnumber them, the Pakistani and Iranian military would simply steamroll them.If they invaded Kazakhstan russia would flip its REDACTED and rip them apart, if they head east china would do the same. The only way we could expect to see Uzbeks invading their neighbors was if the USA or some other world power were using them as fodder kind of like we did with the Iraqi Army against ISIS or Russia using the Syrian military as cat's paws. Uzbeks just aren't very good at taking the initiative. If say, china wanted to use them to push into the middle east, or if Russia wanted to use them as proxies to push their influence south, or if the USA wanted to antagonize Russia or china by establishing a powerful allied power on one or both of these countries doorsteps it could happen. The important thing to remember is that the more powerful nation using them would be what was actually providing the heavy hitting power and deterrent from counter attack.
Uzbeks really don't want to fight anyone, they were only barely able to rally resistance to the Taliban, and the Taliban Pashto had to get pretty well into a genocidal campaign to provoke that response. Uzbeks are by nature pretty accepting and laid back people, their women run around with uncovered faces and they allow Jews and Christians to live unmolested, if its not a direct threat to their existence they just really don't care much. The taliban were less a religious movement and more an ethnic cleansing dressed up in religious rhetoric, the Taliban were really just the Pastho tribes trying to assimilate or eradicate any of the ethnic minorities within Afghanistan, the uzbeks even tolerated them to a remarkable degree until they started killing everyone's wives and children. Final word I would have to say on Uzbeks from living among them is that to get them to fight you need to threaten their existence, and even then they need a ton of help from a more powerful nation. Angels and lucky spirits are fine and well, but it was really our airstrikes and our boots on the ground advising and assisting that carried the day.