It's possible only as a myth, that was a time when the earliest ever of civilizations formed in Northern Iraq, which wasn't Arabic yet. Gilgamesh was Sumerian, and he lived in 2700 BCE.
in reply to Re^3: Do you have a middle name?
in thread Do you have a middle name?
Arabic seems to have come around from Aramaic and has a semitic origin, it appeared much later than the time of Gilgamesh and it appeared in Jordan AFAIK...So there's a mix-up in your statement but many myths were attributed to Arabs when they were rather of other origins because that part of earth was like a cocktail of many different interleaving cultures and influences along the passage of history...