I'm aware of the history of the Chinese Civil War, from the First and Second United Fronts formed to combat the warlords and Empire of Japan respectively between 1927-1945, but I'm curious if there ever existed a possibility for the Red Army to have won the Chinese Civil War before 1931? What factors would have to change for this to happen?
Until 1927, Mao was a supporter of the KMT and Chiang, even on being on one of its senior committees. It was only when Chiang turned on the Communists in 1928 that he began fighting them. Then he was kicked out of the Party's Central Committee in 1928 for what was seen as treachery and cowardice, using the revolution for personal gain, as a result of his actions at Changsha. He ended up in Jiangxi, where he ran his own little fiefdom. When the Jiangxi Soviet Republic was formed in 1930, Mao lost power: the CPC moved to and assumed control of Jiangxi, taking it away from Mao's personal control. The main problem was that other Communist leaders, until they had no choice, didn't trust him. He spent most of 1931 accusing political enemies and rivals of being spies and traitors and purging them to regain his power. It was only in 1935 that he was voted as Chairman of the Politburo, and that was only because Stalin backed him.
Aside from that, as mentioned, there was no single Communist armed force. Chinese politics were a complete mess with multiple competing factions, and that included groups supposedly on the same side. It took the utter defeat the Communists were facing to make them unified; in effect, the Nationalists kicked the ass of the Communists so badly that the survivors had to work together just to have any chance of survival, and Mao was fortunate enough to have been one of the leaders of those survivors, and even then it took the Japanese invasion to weaken the nationalists enough for the Communists to regain their strength and be able to push them back.
Without the war with Japan, the odds were very much more likely that at best the Communists might have been able to hold on to a remote portion of the country, probably with the USSR providing material support, while the Nationalists consolidated their hold on the majority of the country and population. I think it more likely the communists would have simply lost, and China would have become an authoritarian anti-communist state under Chiang Kai-shek.
I think Keith Morrison's answer gives you the things that would have had to happen for your goal to be met.
Mao would have needed to form a coalition of forces that could overwhelm the opposition forces. It would have been most beneficial to his end goal if the opposition remained fractured and non-unified. That would mean that his coalition would need to be a majority of forces, but large enough to consume each of the opposition forces.
It would be beneficial if he adopted the strategies of Genghis Khan and didn't destroy his enemies but co-opted them so they'd fight for him.
It wouldn't matter that much if his initial coalition wasn't made up of communists. The Iranian revolution demonstrated that if disparate groups unify towards a common goal, that doesn't necessarily mean that the coalition will share power. The Islamists and reformists and socialists worked together and overthrew the Shah of Iran, but after the dust settled, Islamists jailed, murdered, and intimidated their way into absolute power. One could imagine that Mao wouldn't have a problem with that solution given the number of his own country he killed after his grip on power was firmly established.