One more time about the uniqueness of Adam and Eve's genome

This could be a question that has already been asked and explained here. But I want to know exactly what restrictions there are on the possibility that in a GAE model, Adam and Eve’s genomes could be slightly different from their contemporaries. On page 84 of the book, Joshua writes,

It is conceivable that God made Adam and Eve with some important biological differences. Only small changes are needed to produce large changes to an organism. However, these differences would not propagate to each and everyone of their genealogical descendants. Their genealogical lineage would quickly spread across the globe till they were ancestors of everyone in a few thousand years. Their genetic ancestry, however, would dilute and dissipate. If their genetic differences were meant to pass to all of the genealogical descendants, then ongoing miracles are required. Speculative and exotic biological mechanisms (such as gene drives) have been proposed to overcome the need for ongoing miracles. There is no evidence of such mechanisms in human biology.

This question assume no ongoing miracles.

Is it impossible that A&E had special genetic material resulting in certain advantageous traits (e.g. consciousness, additional intelligence, etc.) that were passed on to some, though not all, of their descendants? And that their descendants who happened to inherit these traits simply died out?

The background for my question is that in the popular understanding of evolution, every useful trait I have as a human (which differentiates me from similar animals like chimpanzees) must have originated from some random mutation in an individual living in Africa tens of thousands of years, which conferred tremendous reproductive advantage to that individual and his/her descendants, such that now virtually all humans have it. Is this popular understanding completely wrong, or grossly incomplete? Why can’t it apply to Adam and Eve?

I understand that many of our ancestors are genetic ghosts, but does that mean that all the information in my genome that I have in common with virtually every other human being (e.g. being able to multiply 10 by 10) must have come from an ancestor who is not a genetic ghost and identifiable in my genome?

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