Yes the Enuma Elish is the oldest epic record, but in terms of ANE studies it is quite young - Babylon was a far cry from the lives and practices of the Sumerians. There was a vast array of snake cults dotting what is now Saudi Arabia, Iraq and Iran. The Transtigridian Snake Gods came from the Choga Mish plain in Northern Iran, not Mesopotamia. Tiamat is not necessarily a snake god, but she is described as being a dragon or chaos monster in Babylon. Arabia was also known for having a huge array of snake cults for which evidence was almost completely wiped out for all useful purposes due to Islam.

I think it's safe to say that even if El Shaddai (god of Shaddai, god of Abraham) wasn't a snake god there are some interesting parallels, one, he is a mountain god, Ningishzidda who is the son of Ninazu the "grand physician" is called "Hero, lord of field and meadow, lion of the distant mountains! Ningišzida, who ... Hero who, after surveying the battle, goes up to the high mountains!" in the balbale to Ningishzidda which is Sumerian. (See Balbale A: Link)

Tiamat was the mother of all the gods - Anu is considered to be the king of all the gods, but he is third generation!

Links to these gods are all over the bible - Bethlehem for example is probably named after Lahmu, one of the monstrous children of Tiamat, "the muddy one" who fathers Anshar and Kishar (An and Ki, sky and earth) so this may give you some perspective on just how old Tiamat is...how far reaching....

Anything to do with chaos monsters, from hydras to dragons are all the mark of Tiamat.

1-10. Hero, lord of field and meadow, lion of the distant mountains! Ningišzida, who brings together giant snakes and dragons! Great wild bull who, in the murderous battle, is a flood that ……! Beloved by his mother, he to whom Ningirida gave birth from her luxurious body, who drank the good milk at her holy breast, who sucked in lion's spittle, who grew up in the abzu! August išib priest who holds the holy ešda vessels, checker of tablets, who secures justice ……! King, wild bull with tall limbs (?), who directs speech aright, and who hates wickedness! Mighty power, whom no one dare stop when he spreads confusion! Mighty Ningišzida, whom no one dare stop when he spreads confusion!.....