Genesis as we have it was compiled by the post Babylonian Exile returnees to Judah. Moses was long dead by circa 537 BCE.
That those scribes had access to earlier writings is not disputed, but in the absence of manuscripts any earlier than a couple or so centuries B.C (Dead Sea Scrolls) we can only surmise what their source material contained.
It is certain that YHWH was retrojected in to the "Genesis" that they used.