Now, as I hope you know, the United States used a very powerful rocket called the Saturn V to accomplish all this ( I'll skip the Mercury and Gemini rockets, they're like a non-conference game almost). The Saturn V used 3 stages to get to the moon, with the Apollo CSM (command module) and the LM (lunar module) sitting on top. It could sling both craft to the moon in one launch.
One of the reasons why we succeeded at Apollo where so many other gov't programs fall short is because we were in a space race with the Soviet Union. They beat us to space, first space walk, first woman in space, first satellite, first man in space. First everything, for a long time. So we put all our effort into it, and succeeded supremely, with a few life altering failures along the way (Apollo I fire). The Soviets, even though they denied it, never could get their rocket to successfully launch. We went with 5 large engines, they went with dozens of smaller but extremely powerful engines. The problem was that you really needed a good controlling program or system, and they did not.
We beat Kennedy's deadline to get to the moon, twice (two landings in 1969). No DEI, nobody was worried about how many women to send or what color. Well, let's just agree that the people in charge didn't worry about it, and that's all that really matters. Along the way we invented multiple technologies that seriously advanced us as a country. Things like portable computers, aerospace innovation, engine technology, communications.
We got so good at it, we landed 4 more times in the 1970's, (one failure, Apollo 13 that was safely brough home. Cue Tom Hanks).