“the ancient Israelites were recording their history in real time as opposed to writing it down several hundred years later.”
Is anyone making the argument that the Old Testament is inaccurate because we had no evidence of Hebrew writing going back this far?
Even if we have evidence of it, it’s not evidence that the bible was written in this period. Nor, is it evidence that the bible wasn’t written in this period either. We simply don’t know the exact period of composition of all the books in the Old Testament. And, not all of them were written at the same time. Genesis was old even in the time of Moses.
Moses was the author of the book of Genesis, as well as the following 3 books of the Bible (The 4 books are known as the Torah.)