The Old Testament often shows a vengeful image of God, but Jesus came to show us the real image of His Father, and it is love. God gave us free will because we are created in His image and He is free. If we are to become His adopted children, we have to be free. God profoundly respects our free will - He provided it.
God remains with Adam and Eve outside of Eden and there is already, hidden, the promise of the Savior. God doesn't abandon them after their “fall”, but promises His love will be with them (us) always.