I'm just thinking about race from the standpoint of a discrete physical and cultural entity rather than visible types which is the way most people define it. It makes more sense to me to think of race in this way. Relative to white Americans, Hispanics seem like a race - they're clearly "not us" and no one thinks they are, and they are easily lumped together from our perspective.

There probably were relatively pure types at the end of the last Ice Age when most populations were relatively stable and adapted to their local niches. Since the age of civilization with everyone moving around the concept of distinct types has become less and less viable over time. I mean, sure, they still exist visibly but as you say there was already a lot of race mixing even long before the industrial age made people hyper-mobile and it has only sped up since then.

The example you used of Siberians is a classic one - obviously there is Northeast Asian ancestry from across the steppes since a long time. You even see that in the Nordic countries though they never admit it (Nordic blondes with a hint of Asiatic features - most common in Finland but also not uncommon in Sweden, etc). And it's integrated enough that such phenotype variability can skip generations since those are just surface characteristics and any given generation's outward expression can depend on the entire genetic inheritance.