I can’t answer definitively, but I recommend the Jewish Publication Society’s (expensive) series of commentaries. there is some discussion of it there, but there is a strand of tradition in Judaism that the Torah was composed by God thousands of years before the creation, and it was the plan of creation, as a matter of fact. So that would rule out the influence of the E of G.
One Christian commentary observes that the Torah is attributed to Moses. And he was educated in the philosophy of Egypt, which described the creation of the universe as such: a giant egg was flying around, and hatched which produced the universe.
So Moses inspiration is to be contrasted with that, and with those nearby faiths which worshiped animal gods, and such. The Jewish commentary emphasizes the uniqueness of the monotheistic revelation.
But the commentary discusses other theories, such as the documentary hypothesis. It bypasses the significant point that Eve uses the holy name of God YHWH around chap 3 or 4 of genesis, before the Name is revealed to Moses. It’s out of place but the commentary is silent on this point.