Traditionally, Genesis was finished mostly by Moses, having the creation stories and stories of Abraham handed down to him (and the Hebrews) by previous generations.
I think rather than asking about the credibility of Genesis, one should question the credibility of the Torah (1st 5 books of the OT). While narrative books such as Chronicles and prophetic books like Isaiah are shown OVER TIME by the Jews to be inspired, the Torah has been considered by the Jews as sacred and inspired for many generations - at least from 9th century (depending on what date you want to give the Torah).
It's historical credibility boils down to how one believes the world was created and whether the flood actually happened etc. Some are convinced that there is scientific evidence to back creation as well as the flood. It really depends on what you're willing to be open to - whether you want to look into evidence for creation and the flood.
Other than that, Genesis' credibility can be found in its theology. It's the theology and philosophical truths of Genesis that has made the Jews believe in its divine inspiration and, therefore, has given the author credibility.