The thought it that for the most part modern humans and Neaderthals were separate branches of the humanoid family. There was some mixing, apparently, but it would be more correct to say that Neanderthals and modern humans each evolved from a common ancester, and not too far back in each line, or they could not have interbred. A donkey and a zebra can interbreed, as can a wolf and a coyote. Doesn't happen much, but it can.
This preposes that there were a spontaneous creation of some population of Homo Sapiens.
Unless I’m mistaken (and I often am), isn’t Neanderthal actually older than Homo Sapiens? Thus, the logical assumption I’m going from is that a mutation of a Neanderthal mating resulted in Homo Sapiens, and this mutation was adept at surviving until sexual maturity, where it’s progeny created more Homo Sapiens.
And as these Homo Sapiens reproduced, at some stage the obvious differences between Homo Sapiens and Neanderthal, this would lead to a separation of the species. Homo Sapiens being more frail, but smarter would eventually replace the more rugged but less intelligent Neanderthal.