There was no end game to the first space race, the idea of humans on the moon being the finishing line came much later, and mostly after the US had done it and the USSR had failed to. The space race began in 1955, before anyone had even got anything into space, the idea that "we are going to walk on the moon before you" was some kind of goal of the US is absurd.

The first real target of the space race was to get a satellite into orbit.