The tradition that Moses is the author of the first five books of the Bible originates from the Word of God itself. The title “law” does not only refer to the commandments that Moses received at Sinai from God.
Already in the Old Testament it often refers to the whole Pentateuch, the Thora, i.e., the first part of the Old Testament. Compare Joshua 1:7; Joshua 8:31; Judges 3:4; 1 Kings 2:3; 2 Chronicles 23:18; Ezra 3:2; Nehemiah 8:1; Daniel 9:11; Malachi 4:4.
The Lord Jesus confirms that Moses is the author in Luke 24:27; Luke 24:44; John 5:46-47.And Paul who often speaks of the law calls it the “law of Moses” (Romans 10:5; 1 Corinthians 9:9; Hebrews 10:28).
It becomes evident from two passages in the New Testament that the term “law” or “law of Moses” includes Genesis: 1 Corinthians 14:34 can only refer to the divine order in Genesis 2:18 ff; Genesis 3:16, since the law of Sinai lacks an explicit command for women to be subject, and in Galatians 4:21 ff Paul talks of the story of Ishmael and Isaac (Genesis 16; Genesis 21).In both cases he speaks of the law.
Genesis contains biographies of seven believers: Adam, Enoch, Noah, Abraham, Isaac, Jacob, and Joseph. They are important for the divisions of this book.