It’s equally possible that there was more than one or even a day where only people were born and no one died.
There was a low point where only about 2,000 humans were estimated to be alive. Certainly you couldn’t have had someone dying everyday then
https://www.science.org/doi/10.1126/science.abq7487
It’s been significantly lower than 10,000 at least once in history.
Unfortunately there’s a paywall to the article but the free abstract gives you the critical information. And this is among some of the most up to date research on the topic
There’s other recent research that counters this idea. It’s still uncertain. Humans have dipped low before, just probably not levels rivals animals like the cheetah, otherwise we’d show the same genetic issues they have due to the inbreeding of the survivors.
I don’t have a reference to it at the moment, so it’s a “trust me” scenario, but what I found then was through googling (because I used to be convinced of the bottleneck), so it’s out there.
From my understanding of the subject the current consensus is the bottleneck did happen. There’s been fluctuations in the exact number, but under 5,000 is what is most widely supported by the evidence.
The only debate I’m aware of is the exact timing and cause of the bottle neck. It was widely believed a volcano eruption was responsible, but that has become more discredited. It appears the population decline occurred before the eruption and took a significant amount of time to climb after the eruption.
If I recall right (and it may not be right lol) it was timing as well as how many other populations there were. I think the initial discovery and research made some assumptions that what they found was the only people around and that it was a sudden disaster. Just like now we think that the dinosaurs were already suffering for various reasons and the asteroid was just a final push towards extinction over time.
I read the full paper and I’m not qualified to evaluate the validity of the model being proposed but I find the idea that the population was
rather implausible. Implausible things sometimes turn out to be true but models frequently turn out to be wrong so if I were to bet, I would bet on the latter.
Plus, for the purpose of the OP, I think neanderthals and other close relatives of modern humans should count as people even if they have no living descendants.