First of all, we must note that it is more correct to say that the Space Race helped America achieve military superiority than to say that the military helped America achieve superiority in the Space Race. However, we can say that the military did help the country achieve superiority.
For the most part, the Space Race helped the military. The Space Race developed American missile technology that helped it gain superiority over the Soviets. Other technological developments that came out of the Space Race also helped to bring about American military superiority.
However, we can say that the military helped to win the Space Race. Perhaps the most important of these was that the astronauts who took part in the Space Race were military personnel. Men like John Glenn and Neil Armstrong and “Gus” Grissom were all military men who became astronauts. Their contributions helped the United States to eventually achieve dominance in the Space Race.