[romanoderoma]

AFAIK the Sumerian king Enmerkar was ruling the city of Uruk around 4500 BC

That's where my estimate comes from, but I'm not archeologist, I might well be wrong

[thaumasiotes]

Enmerkar appears to be known from the Sumerian king lists, where he is one of the pre-flood monarchs who reigned for hundreds of years.

I wouldn't put much weight on any estimate of when he ruled.