Timeframe issues aside (which are huge, admittedly), there were plenty of 1-heatbeat genetic bottlenecks.
Google:
"Y-chromosome Adam"
"mitochondrial Eve"
Basically, all humans share at least one, and probably more than one, male and femal ancestor.
Of course, they can't say --- with any certainty --- that the given, proven "adam" (a real misnomer) and "eve" (same) lived at remotely the same time.
That said, obviously each of the bottlenecks had parents, who could presumably qualify.
And yes, I am greatly over-simplifying for brevity.
And no, I am not saying that this is proof of Genesis.
Just that the science and the Bible are not inconsistent, which is something both sides of such debates often forget.
Like you said, the timeframe issues are huge. If Genesis is taken as metaphor, then that's a whole 'nother story. In other words, I completely agree with you.
But Adam and Eve would still not be Irishmen!!!