Did any previous events (prior to WWII) contribute to the start of the Cold War?
Although it was the events towards the end of WWII that really got the Cold War started, the Cold War had its origins in the Bolshevik Revolution of 1917 and its aftermath.
When the Bolsheviks took power in 1917, they created a communist government. The communist form of government and communist ideology are completely opposed to the ideas of democracy and free markets that are the basis of US society. Because of this, the two countries would be diametrically opposed to one another in ideological terms.
Because the US was so opposed to communism, it even sent American troops to Russia after WWI. These troops were sent to help fight against the communists in the Russian Civil War. Of course, they were not able to defeat the communists, but the Soviets would not forget that the US had tried to overthrow their government. The two countries would not even have diplomatic relations with one another until 1933.
We should also note that communism is an avowedly expansionist ideology. It believes that communism will take over the entire world. After the creation of the USSR, the "Comintern" was created to try to spread communism across the world. This gave America more reasons to be suspicious of the Soviet Union.
The start of the Cold War should not be a surprise. There had been tension and distrust between the US and USSR ever since the USSR came to exist. Once the USSR became an important player in world events, a Cold War was likely to occur.