[Drammach]

However, most of the ancestors of today's European people (and American Indians and East Asians) lived in an area to the NW of Greater India. This was an ice-free zone and gave tremendous access to big game.

Are you speaking of the Caucasus mountains?
IIRC, there was a large "pocket" of ice-free land during the last glacial period situated in the Caucasus mountain range..

[muawiyah]

Ukraine, NE of Ukraine, and out on the Steppes.

The Caucusus mountains are much farther South, and they would have been glaciated during the last glacial peak. Any part the Caucusus mountains played happened long after the "development" of the European people in Asia.