

This has been modeled. Though I don’t have any references at hand, this is what I remember.
If you want to allow people to choose mates and breed normally, you’d need at least 3000 people, 4 to 5000 would be better.
If you are strictly controlling genomes and breeding pairs, ignoring monogamy and social norms. You might be able to get away with 100 if you selected for maximum initial genetic diversity. But 200 would be easier.



That low end of 100 would be with full eugenics. Selecting for genetic diversity, not for “hotness”.
If you were selecting for that, it would mean less genetic diversity, you might start seeing problems within 5 generations. But that’s just me speculating.