This answer by u/ParkSungJun, about why soviet-sino relations broke down, partly answers why the soviets supported the KMT over CPC initally.

The Soviets recognition of the KMT as the government of China goes back prior to the Second Sino-Japanese War (or World War II) with Sun Yet-sun. The recognition had nothing to do with ideology and mostly for practical reason. The KMT loosely kept the country together and due to United States isolationists policies, turned to the Soviet Union for foreign assistance and military training. In return, Sun Yet-sun allowed CCP members to part of the government. The CCP was a handful of people at the time and the KMT controlled the military, the money and had governance over the country. During Japanese expansion into Manchuria, the Soviets were concern of Japanese expansion into Russian territory so, like the United States, were incentives to keep China afloat against the Japanese during the war, thereby helping the KMT. They even intervened through the Communists International (Comintern) to force the CCP to form the Second United Front with the KMT to fight against the Japanese.

Fast forward several years, and when the Chinese Civil War erupted, by every metric Mao was not suppose to win the war. Chiang had a veteran military, controlled all the resources and major cities, while Mao had peasants and was hiding in the mountains. However, while the Soviets did recognize the KMT, they were also secretly assisting the CCP, financially and militarily. After CCP outmaneuvered the KMT in the Northeast (Manchuria), city after city, the CCP took every major city, mostly without spilling a single drop of blood as the regional generals surrendered and join the CCP without putting up a fight. Chiang fled to Taiwan, the Soviets recognized the CCP's victory and the People's Republic of China as the government of China and the rest is history.