No, it would be statistically inevitable:
https://en.wikipedia.org/wiki/Mitochondrial_Eve
https://en.wikipedia.org/wiki/Y-chromosomal_Adam
"around 200,000 to 300,000 years ago"
although we're not descended from _only_ this one ancestor on each side, we are all descended from that one.
https://www.scientificamerican.com/article/humans-are-all-mo...
Edit: Just to clarify what I'm trying to get at is that there are probably quite a lot of Ancestors That Everyone Descend from.
The nearest "ancestor of all living people" is calculated to 150 000 to 300 000 years ago, depending on which one you're talking about https://en.wikipedia.org/wiki/Mitochondrial_Eve or https://en.wikipedia.org/wiki/Y-chromosomal_Adam
https://www.scientificamerican.com/article/humans-are-all-mo...
My father researched a family tree; not rigorously, like Mormons do, but he spent about a decade tramping around the country, visiting graveyards and inspecting parish records. I have a bound volume of the tree. He claimed descent from (a) William The Conqueror, (b) Lady Godiva, and (c) Charlemagne.
I don't have his records, only the tree. The links are pretty ropey, especially when you reach further back. And he imported big chunks of it from trees built by others. His conclusions seem pretty implausible, but that article makes them seem a bit more plausible.
If you keep track of the number of descendants of that random human who are alive over time, what you'll find is that in almost all cases it either goes to 0 over a short number of generations or it increases almost exponentially until it hits some limit such as a physical barrier that stops growth in all the places their descendants live and prevents their descendants from leaving.
If a few of their descendants can travel, then in their new area their descendants either go to 0 or exponentially spread in the new area.
It doesn't take a super long time, in the case where the number of descendants doesn't go to 0 for the number of descendants to grow to the point where everyone is a descendant of that random human.
But note that the same is true for any other random human we might have picked at that time. Every person who was alive at that time either has no living descendants or everyone now alive is a descendant of theirs.
The same is true for any point farther back than the arbitrary point we picked, because anyone alive at that earlier point who has any descendant who reached the first point will be an ancestor of everyone now alive, because their descendant who reached the first point is.
The most recent point at which everyone then alive is either an ancestor of all now alive or of none now alive is called the "all common ancestors point" or the "genetic isopoint".
Most researchers think the genetic isopoint was somewhere in the range of 4000-15000 years ago.
There's also a point of interest that occurs between the genetic isopoint and the present called the "most recent common ancestor point". That is the point where any two people now alive have a common ancestor at that point, but there are groups of three people where there is no common ancestor of all three at that point.
There's also the "matrilineal most recent common ancestor" and "patrilineal most recent common ancestor", which are like the "most recent common ancestor" except you only counts female descendants or male descendants, respectively. These are also called the "Mitochondrial Eve" and "Y-chromosomal Adam", respectively. These are even farther back than the "all common ancestor point"
You can also look at this going backwards. As you go back the number of logical ancestors you have doubles each generation. But that exponentially growing number of logical ancestors has to map to the almost exponentially shrinking number of people, and so some distinct logical ancestors of yours are implemented by the same physical ancestor. The farther back you go the more people's ancestor trees each physical person then alive is in, unless they are in none. And so you again find the most recent common ancestor point, and the all common ancestor point, and the matrilineal and patrilineal most recent common ancestor points.
If the genetic isopoint really was less than 15000 years ago, you can make some interesting inferences. For instance the Neanderthals went extinct around 40000 years ago. That's farther back than the genetic isopoint. Since some people now alive are known to have Neanderthal ancestors (because they have some Neanderthal DNA) then everyone now alive must have Neanderthal ancestors.
Note that this doesn't mean everyone alive must have Neanderthal DNA. You only pass half your genes on to your kids so you can eventually end up with descendants who don't actually have any of your genes.
Same with the Denisovans. They went extinct before the genetic isopoint, and some modern humans are known to have Denisovan ancestors and we we can conclude that we all do.
[1] I say "almost" exponentially because instead of e^(at) where a is constant, a is variable and has long term been slowly decreasing.
You're quite right; although I was being flippant, rather than confused.
https://www.npr.org/sections/13.7/2018/01/31/581874421/be-hu...
I do wonder how many "single ancestor" bottlenecks humans and other species have evolved through.
That said, I do wonder how sound the research above is. It seems that lateral gene transfer resulting from, say, the first viral pandemic, could be responsible for a common snippet present in all surviving life billions of years later.