Nah, green Sahara ended pretty early in the bronze age. The old kingdom Egyptians were really just getting the tail end of it. It was definitely natural, I don’t think that’s in question; the (non-mini) ice age was simply ending, about on schedule. It would have been a much slower change than what’s happening now.

There were a few trees that managed to hang on in one area, though, with the last being “accidentally” run over by the colonial-era French.