Following the defeat of Germany and Japan, Joseph Stalin told the Soviet people, "the war against fascism has ended; the war against capitalism has begun. Stalin believed that peaceful coexistence between communist and capitalist societies was impossible. There was also the Soviet belief that the communist revolution should be exported, that it would cascade over the entire world. One of the great fears of the American people during the Cold War Era was that of Communist infiltration. Stalin not only refused to withdraw his troops from eastern Europe; he attempted to starve out West Berlin and thereby cause the city to collapse.
So, to answer your question, I think it is obvious that the United States was responding to Soviet expansionism. Indeed, the containment policy of Truman Era was designed to stop the spread of communism. The arms race which ultimately developed was a jigsaw race of one responding to the other. Still, had Stalin not been so persistent to go forward with the Communist Revolution, it is doubtful that the Cold War would have taken place.
Given these two options, America was clearly responding to Soviet expansion. At the start of the Cold War, there was really not any American aggression going on. The US had not made any moves that were directly hostile to the Soviet Union. By contrast, the Soviets had taken control over all of Eastern Europe and were clearly trying to impose communism on those countries.
However, I would argue that the Soviets were responding to something -- they were responding to Russian history. So it's not as if they were simply being aggressive and wanting to expand. The Soviet Union had good reason to want buffers with the West. Their country had been invaded (and almost conquered) both by Napoleon in the 1800s and by Hitler in WWII. Because of this, there was ample reason for them to want friendly countries around them.
Overall, then, I would argue that the Cold War was started by America's (understandable) reaction to Soviet expansion which was itself a (understandable) reaction to what had happened to Russia in the past.