I haven't been able to find that anyone can say who or when the Bible was written. It's a lot of guessing and projecting.

You don't actually know that Genesis 1 and 2 were written by different people. As the scholar Hulisani Ramantswana establishes: "Genesis 1-3 may be properly read as a work of a single author who approached the same subject from different perspectives."

https://www.academia.edu/9859583/From_Bad_to_Good_A_Dialogic_Reading_of_Genesis_1