Earlier quoted context omitted.
The premise was more that we can say with near-certainty that there are non-visible genetic differences between the races without even knowing specifically what these traits are or the extent to which they have diverged. We know this based on our understanding of genetics, natural selection, migration patterns, randomness, and the passage of time. It would actually be quite the story if the races were somehow identic…
Your "extremely likely" scenario is the "cold winter theory", which is problematic for many reasons including the myriad of historical instances where hot-climate civilizations outpaced cold-climate civilizations.
How would you explain how geographically distant groups in radically different conditions could, over millennia, converge on all of the exact same non-visible traits without even minor variations? I truly can't imagine a way that this would be possible aside from the infinitesimally unlikely product of completely random chance.