Moses wasn't the sole author of Genesis. He didn't get an inspired download of Genesis when he became an anointed one of God. There were preserved ancient documents that were given to Moses at the proper time. Noah's log was one of those documents along with the story of Job.
A May 15, 2003 Watchtower revealed there may have been a log of Noah that was passed down through many generations. There are ancient records that say Seth, the third son of Adam and Eve, was the inventor of written language. He possibly was the first one to get the accounts of Genesis started. The early inspired records would have been passed on from Seth to Enoch and then from Enoch to Noah and then to Shem.