Internal evidence in the text of Genesis 1-11 argues strongly that it was composed after the Israelites returned from Exile. Other parts were adaptations of common Mesopotamian myths. The evidence appears below thanks to a well researched post by Jonathan_Burke
He writes:
Most readers of Genesis 1 are hardly aware of its full content. Confined as many of us are by the English text, we miss a wealth of information which is embedded in Genesis 1-11, which would have been completely obvious to the original audience and which comprise an important part of its message.
See his post for the details but he then concludes:
If these chapters did exist as early as Abraham (or at least Moses), then we must explain why they are ignored by most of the books of the Bible, and only suddenly referred to by the post-exilic books. From Genesis 12 to the end of 2 Kings, book after book after book shows no awareness of these chapters at all.
Speaking of post-exilic literature, I ran across this info in Old Testament Abstracts:
Lukasz Niesiorowski-Spano, “Origin Myths and Holy Places in the Old Testament: A Study of Aetiological Narratives” [aetiology = “the story or stories told about how a place received its name”] (International Seminar, 2011).
“Niesiorowski-Spanoʼs monograph examines the aetiologies of a series of extra-Jerusalem cultic sites as related in the Books of Genesis, Joshua, and Judges, viz., Beersheba, Bethel, Dan, Hebron (and Mamre), Ophrah, Shechem and Gilgal, plus the Transjordanian locales Galeed, Mahanaim and Penuel. Basing on the evidence of the relevant biblical texts, archaeological discoveries, and such extra-biblical documents as Jubilees, Josephus, and Pseudo-Philo, N.-S. endeavors to trace the tradition-history of the aetiologies in question and their final literary fixation, as well as the nature of the cult (and the deity worshiped) at the given site. On this basis he concludes that the materials studied by him, while they do—in some cases at least—draw on older materials, received their final redaction in the Hasmonean period (160-110 B.C.), the territorial realities and aspirations of which they reflect. The fact that the Jerusalem priests responsible for these materials included such accounts accrediting the sacral character of an array of extra-Jerusalem sites would indicate, according to N.-S., that Jerusalem was not, in fact, regarded by them as the sole legitimate place of worship—Jerusalem attained that status in Judaism only after the catastrophe of 70 A.D.”