Under Eisenhower, the DoD dropped the F-1 as superfluous, but von Braun was developing it for a future moonshot, and took it with him to NACA, which became NASA. Big booster designs using one, two, three, four, and five F-1 engines were drafted by and/or for von Braun to pitch, and when JFK got pissed off about the seeming superiority of the Soviet space program, von Braun took his F-1 right to the head of the class. The Apollo program started under Eisenhower. JFK gets way too much credit.

This picture was taken in 1960. While those aren't F1's, that is a Saturn booster.