I've had similar ideas and thoughts. I've even speculated that they (the Tarim people) were refugees from the salt water flood of the Black Sea 7,600 years ago.
Now, I'm a Dane who went to Ireland and stayed (maybe a Viking) in ancient times but my Grandmother's DNA is the same as 9,000 year old Cheddar Man found in England.
There's also a 23,000 year old Cheddar Man too.
So...Caucasians have been in Europe for at least 45-50, 000 years if not longer.
Here's the DNA map of my R1b yDNA.
I believe after the glaciers melted there were lakes in the region that made it more hospitable for settlement.