3K years ago, human brains were that large, with heads big enough to accomodate them? 3K years is not really that long, anthropologically speaking.
Were the typical heights different than now?
I always thought average people were slightly shorter then than now, perhaps only 5ft 7’ tops for the men.
So how could a man only 5ft 7’ support a head the size of a
Georgia Watermelon? Bobble-headed Barbarians?

Much depends on the diet.
Both Euorpeans and Japanese have gotten much bigger when their diet was improved to include more protein and fat, especially when young.
It is one of the reasons nobility were often larger than the peasants. They simply had a better diet.