Of course, the Cold War had barely gotten started in 1945. However, at that point, we can say that the US was ahead of the Soviets, but had not beaten them in every way.
The Soviets were ahead of the US in at least one or two ways. They had taken control of Eastern Europe. They had managed to push into half of Korea. In short, they had gotten significant territorial concessions from the West.
The US, however, was ahead in military and economic terms. The US was by far the richest country and the one least damaged by the war. The US was the only country with the atomic bomb. In these ways, the US was leading in the Cold War when it started.