The Redstone family of rockets were originally developed by the US Military to transport Intercontinental Ballistic Missiles during the Cold War.
After the formation of NASA in 1958 by President Eisenhower, Project Mercury was announced. This program was designed to develop the capability for Americans to fly in space.
To get there, NASA adapted the Redstone rocket to create the Mercury-Redstone Launch Vehicle (MRLV) otherwise known as Mercury Redstone.
It was this rocket that transported a chimpanzee called HAM into space on 31st January 1961. This was was followed up four months later the rocket listing Astronaut Alan Shepard into space, earning him cult hero status by becoming the first American to reach orbit.
However it was a bitter sweet moment for America as they had lost out to Russia by just over one month in getting a man into space for the first time, with Russian Cosmonaut Yuri Gagarin orbiting the earth in April 1961. It wasn’t going to be the last time that America was to loose out to Russia in the Space race. Practically every major milestone of new human achievement in space was achieved first by Russia up to an until America put a man on the moon.
This achievement was so spectacular in itself (to this day, America is the only entity ever to send human beings outside Low Earth Orbit) that it can be argued that American ultimately “won” the so called Space Race, however without the competition between America and Russia in space, it’s virtually certain that there would have being no race to the moon at all, and for that, both space programs should be very appreciative of each-other.