Won't fly IMHO. Wernher von Braun is dead. We both know it was not the US Moon program. It was a German Nazi one. You may try to argue like "but wait, the first man at the Moon was a US citizen!"
Man, the first survived live creatures in space were Soviet dogs Belka and Strelka. So the phrases "American Moon program" and "Doggy space program" are absolutely equal
To sum it up: Soviet commies used dogs for their space program. German Nazis used Americans for their Moon program. Actually Nazis used not just Americans as a labor and experimental mouses for their project. They also used the American money.
Of course they've been there. But the same way as Soviet Belka and Strelka dogs. So when we speak about the Space program, it was totally won by the Soviet Union: first Sputnik, first dogs and only after that, a first man in the outer space (both inside a spaceship and outside). As about the Moon program so it doubtfully has a single winner because:
1) The first pictures of the Moon's "dark side": Luna-3 robot sent by the Soviet Union.
2) The first successful Moon landing: Luna-9 robot sent by the Soviet Union.
3) The first samples of the lunar soil: Luna-24 robot sent by the Soviet Union.
4) The first human at the Moon: American citizens sent by German Nazis (von Braun was an SS officer).
These are known facts nobody should argue with and there is no 100% winner in the Moon race... as you can see.