After the Second World War, tensions between the two power began to rise. One way this happened was in their possession of bombs.
In 1945, the United States was feeling secure in their position, as they were the only one with the atomic bomb and they thought the Soviet Union was still a decade away from it. However, they underestimated the Soviet Union, who had it by 1949.
The Hydrogen bomb followed in 1952 for the United States and 1953 for the Soviet Union. Between these developments and the military alliances they were creating, the two countries reached superpower status as they were thrust into the Cold War.