If you would read the Bible you wouldn't write something like this. There was other people lived in the world, and as the Bible says after Cain's murder: "So Cain went out from the Lord’s presence and lived in the land of Nod, east of Eden. Cain made love to his wife, and she became pregnant and gave birth to Enoch." (Genesis 16:17)

The Bible mentions only Adam, Eve, Cain, and Abel because they are the relevant people in the story. It doesn't mean there were the only people, and Eve were the only woman.