Yeah, population sizes overall would have been much smaller in the past, so paleolithic times would probably be comparitively insignificant (even 2000 years ago the entire population was less than 200 million and now it’s 8 billion more than that).

True, but it was also an unfathomably long time, so IIRC it cancels out. Uhh... nope, I remembered wrong. Per OurWorldInData, pre-agricultural people about equal living people in count, meaning about 15% of the total. I'll cross that out.

I wonder if you could get a very rough statistical estimate of humanity’s downfall just by assuming that we are somewhere in the middle of history

I feel like I've seen this done. Yep, it looks like it was a guy named Richard Gott that first wrote about it in the 90's with respect to population, while the whole concept is called Lindy's law.