Our current understanding of physics dictates that the (observable) universe has a finite size and a finite lifespan, from which it logically follows that there can't be an infinite amount of humans.
If that's genuinely the basis for this reasoning, it only makes the argument seem even more dubious to me. If the statistical argument is really so sound, it shouldn't have to rely on our understanding of cosmology.
Also, is there no phenomenon here where a sufficiently large N becomes increasingly indistinguishable from infinity?
The entire universe could very well be infinite, with infinite “Earths” and “humans”. In which case the argument doesn’t work since you can’t choose uniformly from an infinite set.
Our current understanding of physics dictates that the (observable) universe has a finite size and a finite lifespan, from which it logically follows that there can't be an infinite amount of humans.