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.

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...