What if the Book of Genesis had been lost and only recently rediscovered? Had the canon started with Exodus, I doubt the skeptics would be any more willing to concede belief. For all their focus, partly because it is Christians' focus, on the unlikeliness of the events of Genesis, nonbelievers would simply transfer that to other miraculous or unusual events: the burning bush, the Red Sea, Elijah and Elisha. There are plenty to go around in the rest of the Bible. Despite the predominance of historically-attested places such as Egypt and Canaan, as opposed to Eden and Melchizedek's Salem, I doubt believers would be cut much slack.
Believers, both Jewish and Christian would look at the Scriptures differently. We would likely regard the Exodus - Malachi set as complete, and the scattered references to Genesis events in the rest of scripture seen by some as intentional and meaningful on God's part. We aren't meant to know...YHWH ordained that some things should remain mysterious... I don't mean to overgeneralize - there would likely be a variety of opinions on that score.
We would be the ones resisting Genesis at first. Yes, yes, it includes stories about all the Abrahams and Adams we are told should be there, but they don't act right. They do strange things. And there are lots of extra characters we didn't expect. This is clearly a book related to the biblical story, but there's no reason to think it is Holy Writ. I believe the power of God's voice would eventually force itself upon us, as believers would be unable to let the words go and would gradually come to accept them, but it might be grudging and take a century.
In that instance it might be the secular scholars who attempted to convince us to take on the new book. As with the spurious gospels we are led to believe are just as good but arbitrarily declared non-canonical by powerful and close-minded early Christians, this Genesis document would be touted by secular critics. They wouldn't credit any literalness to the individuals and specific events described, regarding them as folk heroes or composite figures. Yet the overall picture would impress them, I suspect. The Flood is there; an account of one tribe rejecting polytheism and human sacrifice shows up in the expected time and place; The conflict between planters and herders shows up in Cain & Abel, Eden turns out to be dramatically near the first places that humans domesticated animals, made shelters, and planted crops, a plausible account of famine driving Jews into Egypt would provide a likely explanation, and a wealth of customs, attitudes, and objects referred to would illuminate all other knowledge of the time and place. Most dramatically, the similarity of the order of creation to current scientific knowledge would be regarded with amazement, as it is unprecedented in the creation story of any other culture. The Francis Collins and Antony Flew style of nonbeliever seeking after truth would produce converts to the faith amazed that the ancient document got so much correct.
Nonbelievers would be pressing Genesis upon us for consideration, in contrast to the enormous energy put into disproving it now. Believers, in contrast, would be overcautious.