Would it have been possible for sin to enter the world if the tree of knowledge of good and evil were absent? I’m inclined to say no, but I’d be interested in your opinion.
Since the Father and the Son worked out the plan for the redemption of mankind before the creation of the world (1 Peter 1:20, Rev. 13:8) and thus well before Adam and Eve were created, had the tree of the knowledge of good and evil not been present in the garden, Satan would have found some other means to cause the fall of mankind. Their disobedience did not take God by surprise. He saw sin entering the world before it happened and had already put His remedy in place.
Remember, knowing the future is not the same as controlling it. Having given Adam and Eve the power to choose, God could not prevent them from exercising it. But He could make advance plans for reversing the consequences of the actions He knew they would take.