How unethical are we talking here?
You could get away with a much smaller starting population if you selectively bred and tried to maximise the output of your starting populations and you enforced cycling partners in order to minimise incestual combinations. You could return to normalcy eventually.

If you're going to be humane, you need a whole lot more. If you're in limited conditions (IE you can't just have every woman give a child to every guy and expect to have everyone remain fed) you need a whole lot more.


Other than that, I'd be interested to know if there are people that don't have any bad genes and who could interbreed frequently without any issues for many generations.