For the Genealogical Adam Hypothesis to be considered as worthwhile science inquiry, it will need to be tested. Fortunately data does exit to do a first-order test of the hypothesis.
First order test: Show that the genealogy of every human being that got its DNA sequenced (over a million people) has in their genealogy a man who live within a one hundred kilometers radius of present day Israel, 10,000 to 4000 years ago. Note that there are whole genome sequencing of ancient people who lived in this time and place.
If you can show that this is indeed the case, it would show that it was indeed possible that a man in this region and time frame could be your sought after Adam. It would not show the person is actually Adam of the Genesis story but it will go along way in advancing the hypothesis.
However, if it is shown that no person of the region at that time period isn’t in the genealogy of every living person today, that would strongly disfavor the hypothesis. It still isn’t a proof that the hypothesis is false, it just says that more data is required to either support the hypothesis or falsify it.
This seems like the kind of scientific research that JTF might fund. It would require access to the DNA data of Ancestry.com, 23andme, and David Reich’s lab and then a whole lot of DNA computation servers.