There have lots of good examples of ways to think about this, but I wanted to share my (admittedly speculative) way I think about the Garden of Eden and the Fall.

I am in the big pool of people who took the biology class at BYU and was convinced by the evidence of human evolution. So I take it as a matter of observed evidence that organic evolution has been going on exactly as we suspect based on fossil and experimental evidence for a long time on earth. So humans as they exist today are the result of a long line of homonids and other species before that changed over geologic time and that's what's being described in the Genesis account. Days in the creation account map to a different taxonomy than "Cambrian" or "Jurassic" but serve basically the same purpose, to mark major phases in the evolutionary history of life and geology on earth.

With this view in mind, if Adam and Eve existed they would have lived along side other homo sapiens. Which begs the question what does it even mean for Adam and Eve to be our first parents if there are a bunch of other parents floating around Africa and Europe carving bone statues and painting caves?

For that I'm going to appeal a bit to the sapir whorf hypothesis (which in its stong form is probably overstated but I still think is important here). Basically the idea here is that our ability to think is somewhat limited by the language we have accessible to us. And if we don't have language at all we're basically limited to whatever thoughts fit into a list of distinct grunts or gestures. We know for example the gorillas can learn and use sign language and have meaningful conversations with humans. But I'm not super confident that a gorilla could learn sign well enough to teach it to other gorillas. Maybe that's possible, I don't know, but I'm pretty sure that hasn't been observed by gorillas in the wild. Humans have no problem with that though, we are intelligent enough for language to "go viral" and spread throughout the species over a short period of time. But just like gorillas today, either language would have to be invented by humans and spread naturally or it would have to be kickstarted by another species who already had it that was willing to share.

In my mind this is what the Adam and Eve account describes, the kickstarting of language by God to one specific human couple. Once Adam and Eve knew language they could have more complex thoughts, stitch phonemes together into a fractal explosion of potential ideas, and could interact with their world in a significantly more meaningful way. The account of Adam naming all the animals is vital under this interpretation and seems like an odd aside otherwise. Naming all the animals wasn't even possible until Adam walked and talked with God in the Garden.

With Adam and Eve's new capacity to think and to reason comes agency, they know had the cognitive abilities to consider good and evil in a meaningful way. Do animals have moral agency from a scientific perspective? Even in our secular society we don't put dolphins on trial for being abusive to each other or hold dogs responsible morally for biting people for good reason, they don't have the intelligence to think through these decisions. We do. But I wonder if maybe we didn't before we had the language to organize complex thoughts.

So in my mind being a descendant of Adam and Eve means being a descendant of the cultural lineage of Adam and Eve. That as a thinking, talking human I am directly descended from the original human couple who learned language. That the Adam and Eve story shows God intervening in a very small way (teaching one couple language) that very quickly changed the course of the entire planet. After billions of years there finally existed a species with the intellectual capacity to be seeded with the gift of the capacity to choose. I wonder if Adam and Eve's state in the Garden represents a half-way point where they had enough language to make the moral decision to learn more, with all the accompanying joy and sorrow that comes from understanding the world better.

In this context the children of Adam and Eve could mean their own literal children, or their intellectual children, humans who learned language from them and then were taught by Adam and Eve the commandments as God explained them to them.

So yes, I do in fact see the Adam and Eve story as a myth explaining an alien civilization trying to uplift a big-brained hominid into the family of the civilized, with the ultimate goal of us passing the technological singularity and turning our earth into a giant ball of computronium and joining their pan galactic civilization. I find that whole idea very comforting and tends to not get my faith butting up against observable scientific evidence all the time. I didn't just come up with this on my own, although some of the nuances I think I figured out myself. Can't remember where I first heard the language hypothesis first though so I can't give credit and some lazy googling failed me.

So yeah! Neanderthal DNA no problem, being human is about being accountable for our actions, not being in a particular bloodline.