Once NASA had a reliable launch platform, the rest was a doodle. And the tens of thousands of observers who were in Central Florida for the event were eye-witness to its success.
From: https://www.fastcompany.com/90375425/apollo-11-landed-moon-how-you-can-be-sure-sorry-conspiracy
"...If the United States had been faking the Moon landings, one group would not have been in on the conspiracy: The Soviets.
The Soviet Union would have revealed any fraud in the blink of an eye, and not just without hesitation, but with joy and satisfaction.
In fact, the Russians did just the opposite. The Soviet Union was one of the few places on Earth (along with China and North Korea) where ordinary people couldn't watch the landing of Apollo 11 and the Moon walk in real time. It was real enough for the Russians that they didn't let their own people see it.
That's all the proof you need. If the Moon landings had been faked - indeed, if any part of them had been made up, or even exaggerated - the Soviets would have told the world. They were watching. Right to the end, they had their own ambitions to be first to the Moon, in the only way they could muster at that point.
And that's a kind of proof that the conspiracy-meisters cannot wriggle around...."
Third-party evidence for Apollo Moon landings
https://en.wikipedia.org/wiki/Third-party_evidence_for_Apollo_Moon_landings#Independent_evidence
Sonny Mathews was a top launch engineer for the Saturn program. He was raised in Humphrey, Arkansas (near Stuttgart), one of seven children, and went into the Air Force and MIT. From the sloughs of Arkansas to MIT was something of an American success story and the Saturn program made it more so.
Thank you for explaining something of the complexity of the launch vehicle.