Without getting into the issue of how much of Genesis is historical and how much is wishful thinking:
The Babylonian captivity, which can be independently verified from archaeology, was 580 to 530 BC. That’s when the Hebrew Scriptures as we know them were consolidated.
Omri is the first independently verified King of Israel, and he was around 880 BC.
Our first historical evidence of the Greeks is in Linear B, which goes up to 1200 BC; but the era of the Ancient Greeks as we know them starts with Greek writing, around 770 BC. Any Greek you’ve heard of by name, other than Homer, is 7th century BC or later.
So the era of the ancient Greeks starts two to three centuries after David (if there was a David), and a lot longer than that after the Flood (if there was a Flood).