One of the great linguistical mysteries has been the origins of the Basque language. Is it starting to fit into the Dravidian sources you reference?
True about cuneiform - the oldest written document is said to be an inventory list or receipt IIRC.
One of the main refugia was located right there at the Pyranees Mountains ~ another on the Dalmatian coast and another in the Middle East.
Obviously there were others in the East.
DNA studies show clearly that Europe was repopulated after the Ice Age by people from the refugia.
One of the more intriguing things to come out of the earliest scientific studies of languages was that when folks migrate away from the core area their language remains fairly unchanged from what it was like at the time of migration. The changes take place back in the old homeland.
We have enough time here for European refugia speakers to have spread all the way from Spain to Scandinavia to India and then back, with their core language fairly unchanged ~ and all that before the first Indo-European drew his first swastika in the dirt near the campfire!
In the meantime the original language would have morphed into the Basque we've all come to know and love, which is a far different language than any of the Dravidian group, or the Fenno-Scandian group! It sure ain't Hungarian either.