I'll lob a shot at this.
1 Oct 1945.
I don't see Truman having any desire to start a war with Stalin. There wasn't anything for the US to gain in doing so.
Churchill didn't trust either Stalin or Communism. But he knew without the US, support, he could not challenge Stalin. He also had the issues with the different colonies clamoring for their independence, and knew that they would not support another war. In fact, it could lead to open revolts.
On to of that, both the UK and US are democracies and capitalist and their people are ready to put down arms and get back to their civilian lives.
Stalin had a great desire to bring all of Europe under his control. He also had an eye on Asia. While he really didn't want to, perhaps he could strike a deal with Mao that would unite the two countries. Whether he was able to or not, he would support Mao and the Chinese communists in taking control of China.
Taking Korea, Western Europe and China would not take a great effort. The closest that Korea had for an army was the communist army under Kim-Il Sung. The Americans hadn't had time to get any troops into Korea yet. The Japanese troops still there were a non-entity. Europe was much the same. The Germans were defeated, her army disbanded and were more focused on rebuilding their country. France had an army, but were still trying to recover from four years of German occupation. Same for Italy.
His two biggest worries were 1) The US had detonated two atomic weapons against Japan, destroying two cities. The USSR had a strong air force, but if a single bomber got through, Moscow, or any other Soviet city could be quickly destroyed. His other issue was that he had little hope of being able to take either Japan of England. The Soviet navy could not, at this time, challenge either the Royal Navy or the US Navy, little lone their combined force. But with an army of over 20 million and his economy geared to support the war, the Americans and British wouldn't be able to return to Europe or eastern mainland Asia. Plus, the British and American people would not have the stomach to fight another war.
He ordered his armies to attack on Oct 10th.