If you can go back and time, then do it right. Go far back to the garden of Eden and kill Eve before she can touch the forbidden fruit and corrupt Adam. All problems solved.
If both god and time machines exist, I doubt he would let you do that.
Also on a side note I think it was god's plan all along to get us kicked out of garden eden. Think about it, god made Adam and Eve, the apple and the snake and he even created a space outside garden eden where we can live.