I disagree with you that the existence of God is factual. There is no physical or empirical evidence of God, no factual proof that God exists. Prophets and mystics have had and do have visions and dreams or feelings of a Divine Presence. I support Matthew Alper's argument that these are the product of the mind as he proposes in his book, "The God Part of the Brain":
"From the dawn of our species, every human culture-no matter how isolated-has believed in some form of a spiritual realm... this is no mere coincidence but rather due to the fact that humans, as a species, are genetically predisposed to believe in the universal concepts of a god, a soul and an afterlife. This instinct to believe is the result of an evolutionary adaptation-a coping mechanism-that emerged in our species to help us survive our unique and otherwise debilitating awareness of death."

I agree the idea of souls is absurd. And, I didn't say we were directly descended from Neanderthals. My whole point was to confound the issue of souls and Adam and Eve. As there have been other species of humans in the past, and certain times in prehistory where multiple species of humans existed concurrently, any attempt to narrow down who first got a soul and who were Adam and Eve is preposterous.

When I was a Christian that was the kind of thing I liked to answer. And here was my (inaccurate) answer: there are two accounts of the creation of men in the Bible. In the first (Genesis 1), mankind is not differentiated from wild animals. So these would be all hominids, including Homo Sapiens. I didn't know if they had souls, probably so... who cares? Now, the second account (Genesis 2) talks about one couple treated in a special manner in a separate place, given the gift of God's presence. When Adam and Eve are expelled from Eden, they meed the other humans.

That account is not true, but it can be compatible with science and what the Bible says -- and is still unfalsifiable. That is why I strongly recommend that you do not go to something that contradicts their beliefs, but rather question how these beliefs were acquired and what could change them.

If Adam and Eve existed, either they weren't Neanderthals or they weren't our ancestors. (Homo sapiens is not directly descended from Neanderthals). Anyway, the whole idea of souls is absurd.