The event that marked the beginning of the Cold War in the space, also called Space Race, was the launching of Sputnik I by the Soviet Union un 1957.
The space race was a competition between the United States and the Soviet Union that lasted approximately from 1957 to 1975. It involved the parallel effort of both countries to explore outer space with artificial satellites, to send humans into space and to pose a human being in Moon.
Although its roots lie in the early rocket technologies and international tensions that followed World War II, the space race actually began after the Soviet launch of Sputnik 1 on October 4, 1957.