Yes.
People point out recessive issues popping up due to inbreeding, which is definitely a factor. But this is really only an issue when a few handful of each generation survive, increasing the chance that every member of the generation inherits the same gene. If a single couple (generation 0) produce 4 children, then generation 1 would have no issues and 25% of generation 2 would have issues, that’s 2 of the 8 members for that generation. A dozen generations later, there absolutely would be some problems popping up and the population would be overall less healthy than the current one, but at that point you’re looking at >1000 people.
If the question was phrased “could a 1000 people repopulate the earth” the answer would be a resounding yes.
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