Another estimate I have seen was a remaining population of perhaps 10,000 people. At any rate a very small number, and from other things I have read, it was not until 20,000 years later that the human population had really begun to rebound.
10,000 is probably the upper limit.
When you think about 7,000,000,000 on the planet now, even a global population of 5,000,000 seems pretty small.
But wipe out all of them except 10,000 and you know what you’re talking about!
Most who survived were probably in the tropics and South Africa. I don’t think anyone emigrated to South America that early.