Sure. They had a creation mythos like everyone else. What they didn't have is evidence of a real precursor civilization to ground those myths. The classical Greeks could see Mycenaean ruins.
Not as many as later civilizations but there are buildings that likely pre-date the Sumerian civilization like the desert kites. And in Syria and Turkey there are megaliths and ruins which are older than Sumer which builders the Sumerians might have know of from oral history.
> The classical Greeks could see Mycenaean ruins.
Apparently, they Minoans had plumbing in the 1800s BC, so I'm sure the Greeks would have been surprised at what had preceded them by a long time.