The US was not a bastion of technical capability or well educated people in the 1950s. To say that the "skill doesn't exist anymore" suggests a misunderstanding of "where it comes from" in the first place.
You can do the same thing for Apollo as you can for the Shuttle. The process of reading through these histories, from front to back, is incredibly enlightening, and shows just how with determination alone you can build something like this from scratch.
That being said.. it really also helps if there's a dual purpose use for the military.