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Um… 400 years is rather low. Even for optimal. But realistic is more like 1000’s.
Hitlers idea was to keep killing the people with the wrong genetics for as long as it took. Hand him nukes and he could clear people a lot faster at the cost of getting some of those he wanted to keep. I bet he would have been willing to trade. Mars… no idea what you are talking about. No one has ever suggested mars could outbreed earth. Muslims… the fearmongering I hear is that they will pollute the culture by bringing their own. Don’t need to outbreed for that. And mixing of cultures is a good thing, not a bad one. That is the real reason those people are wrong.
For most of history, people were dying of bullshit about as fast as they were made, especially the kids. OP didn’t specify if that comes back, and a few hundred is what a premodern birth rate gives you without it. Relatedly, 15% of everyone who’s ever lived is still alive, because growth has been so fast since we figured out how to stop, like, plagues.