The leading thinking right now is that they evolved in Europe and Asia, not Africa. There is an interesting map about 1/4 of the way into this article.

https://www.nhm.ac.uk/discover/who-were-the-neanderthals.html#:~:text=When%20did%20Neanderthals%20live%3F,physical%20evidence%20of%20them%20vanishes.

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I am not expert about non-African hominids, but I guess this implies that there were already some/many hominids outside of Africa leading up to Neanderthal. We (homo sapiens) were just a branch that still evolved in Africa.