The alliance of the US and the USSR during WWII was very much a marriage of convenience, especially for the convenience of the Soviets. After the war, competition took off in so many directions, it’s hard to identify them all. The US already had nuclear weapons, but the Soviets got into space first. I think it surprised the US that the Soviets managed any of this, because they had suffered such direct losses in the war, and were still recovering from their own civil war. (In 1974, I was told that every person then living in the USSR had lost someone at least as close as an uncle in the war.)
Think too of the different ways the US and the USSR dealt with the countries in their spheres of influence following the war: The US could mostly help longtime allies recover, but from a distance, and these were strong and rich countries to begin with. The Soviets dealt with a number of countries that had been client states since tsarist times, and nations that had been directly claimed for a Nazi empire. And most of these countries had histories, like the SSRs, of authoritarian government. So it was easy for the Soviet Union to spread its brand of authoritarianism across Eastern Europe and into Central Asia. This swath of authoritarian control looked like a big challenge to the US.
Of course, just plain politics came into it too, US politics viewing the presence of Communists in the US as a threat. Once you view another nation as your world rival, and expect espionage to be widespread and deep, the tension is bound to rise. We’re just lucky it didn’t reach a breaking point.