Well, regarding the able bodied people left over…:
Women. The building up again was largely done by women. Most men either were dead, maimed or still in war imprisonment.
There is a recognized German word for these women and the hard work they did: “Trümmerfrauen” (rubble women).

But apart from the very hard early years, I think the transition back to “normal” went surprisingly fast.
After all, the core of Germany still was the remains of the probably most industrialized nation on Earth at the time, and a lot of the infrastructure was outside of the devastated main city centers and could be reactivated again rather quickly.

Also, with the cold war starting, the winning powers (mainly the US on the one side and the USSR on the other side) took a huge interest in bringing the parts of Germany situated in their respective regions of influence back to some decent level of economic and industrial standard (as opposed to forcing the whole country to become a de-industrial agrarian country, which had been one of the proposals before).

I unfortunately don’t have any readily available links to material about the time, but I suspect that there must be a lot available.
The “Wiederaufbau” (“reconstruction”) and “Wirtschaftswunder” (“economic miracle”) time and the whole early cold war in Europe with the two Germanys and Iron curtain is fascinating time period after all…