Essentially what they did back in the late 60's took some major balls. There were massive risks, and they did it and did it successfully and I think that's what makes it so hard to believe.
For example, it's probably well known than Apollo 8 was the first manned trip around the moon. It's easy to forget that the USSR and the US were locked in a space race, and we were losing for about ~10 years. From about 1957-1966 the USSR kicked our tails in almost everything space related. First satellite, first man, first woman, first orbit, first probe to the moon, first to photograph the backside of the moon. First space walk.
It wasn't until about 1966 and the Gemini program that we were at least on-par with our Soviet Counterparts and actually began to exceed their capabilities. First orbital rendezvous, first docking, first long duration mission (two weeks in a Gemini Capsule).
The Soviets were well on their way to being the first to put a man around the moon, and in fact they had already sent a spacecraft full of animals (turtles and other small animals) around the moon with their Zond spacecraft. They didn't need the N1 to do this, they already had the capability.
NASA made the decision to send the first full-stack Apollo V around the moon because the LM was not ready. Remember, this was December 1968. The Soviets were very close to sending Zond on the same mission, but they were having issues. The 2nd and 3rd Zond ended in failure, mostly due to navigation errors and technical issues that would have resulted in LOC (Loss of Crew).
Instead of sending a test Apollo full stack into space or even an unmanned test they send full crew, three men. This was ~2 years after the loss of Apollo 1 crew in a fire on the launch pad. They launched it, sent it on a non-free return trajectory (not even Artemis II will do this), had to use the big CSM engine twice. Once to orbit the moon, and once to return home.
BRASS BALLS