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For a future blog post, as a non engineer I'd be curious how an engineering team designs a system (like those you detail) and others in that mission when there is no way to test them fully in advance of the mission. I know that's a very basic general question but essentially how to you know a hypothesis you can't test works (even with various degrees of pre-testing and scientific knowledge. I am not talking about that 'we know that sound travels' or things that are known but things you are pretty sure but not absolutely sure until you have actually done them. (I do know things are done in stages with various testing and small steps but I guess I am unclear on how once lives are at stake (meaning liftoff from the moon) you really know 'it will all work as planned' meaning to a super high degree of likelihood enough to take the risk.

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Soviet (Russians) don't fully test systems in few programs, including first Moon automatic flights and R-7 rocket.

BUT! Because of this, R-7 made first successful flight from 7 or 8 try, and the same was with first soft landing - 6 ships crashed before success.

Other programs, like Buran or Lunokhod, was tested on small analogues or on bench. Examples: for Lunoknod created web wheels for Russian all-road truck, and it made thousands off-road kilometers; for Buran was created few ships analogue, program named "Bor"; for rockets, usually created prototype from parts of previous generations rockets, looking Frankenstein.

When create analogues was impossible, created very simple designs, just like programmers create micro-kernel systems.

And in nearly all Soviet human programs, except "Voskhod" (sunrise, their success I think just luck), used rule, that ship should make 3 fully automatic flights without strict remarks, before carry human.

And yes, Soviet space program was more automated then American. - Soviet ships was capable to make all things without human on board. And they even made automatic flight around Moon without humans, but all flights had big problems. But Leonov said, if human was accepted, he would be fight for survival and made success (he was really brave).

Testing the systems for Apollo was a huge task, more than I can describe here. Everything from component testing to putting a Lunar Module in a giant vacuum chamber on Earth. Each flight pushed things further so they could test in Earth orbit (Apollo 7), then Lunar orbit (Apollo 8).

For the ranging system specifically, they could do most of the testing on Earth. As long as they could predict the antenna behavior at long distances, everything could be tested pretty accurately. In addition, the Apollo Guidance Computer provided the same ranging data in a completely redundant way. So even if the ranging system completely failed, they still had a backup.

How did the AGC have the same ranging data? I thought it was a completely different system.

The AGC computed the position (including range) using inertial guidance and star sightings by the astronauts. So yes, it was a completely independent system, but the results should be the same.

I guess Apollo 13 had to rely on the LEM's guidance computer for ranging, because the command module was powered down?

As the article below explains, it's a combination of structured qualitative analysis and a review process. That process builds on top of all the other application-specific or discipline-specific processes, like a hierarchy. The higher up you go, the more generic it gets. The lower down you go, the more you critique the exact math or test or whatever.

https://adsabs.harvard.edu/full/1996ESASP.377...83F

For the Saturn V rocket/Apollo as a whole, The Saturn V Story documentary is quite good. It's on Amazon but I'm sure can be found elsewhere.

The short answer is that, as you say, things were done in stages, problems were found and fixed, people did die (the Apollo 1 fire), and the Apollo 11 moon landing was a pretty close thing.

you can artificially create RF channels with long delays for bench testing a system like this

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