3700 years is enough to build a large population.
Also, they had the knowledge technology/science exists. So it's a bit hard to swallow they didn't start to rebuild some of that from the very start. The ones coming back to earth are astronauts for God sake. They are among the better minds, super trained, able to perform many tasks to completion. They have two docs, a former teacher and scientists and they are not able to build/start something the first 10/20 years ? Not even able to pass that knowledge to the first children ?

As for the beam: good luck managing several billion people waking up naked in the middle of nowhere, when over 50% of them are city animals and do not know the first thing about survival.
You really need to do it at a manageable pace, by building everything you need slowly. Bonus: stone people can wait a very long time if they are not broken, so you have time to bring them back.