What would the world be like if Adam and Eve had not sinned? Would it only be a matter of time before someone else after them would have sinned?
It would be impossible to speculate because we don't have sufficient information. We know that God planned on the fact that men would sin and need a Savior. "And if you call on the Father, who without partiality judges according to each one's work, conduct yourselves throughout the time of your stay here in fear; knowing that you were not redeemed with corruptible things, like silver or gold, from your aimless conduct received by tradition from your fathers, but with the precious blood of Christ, as of a lamb without blemish and without spot. He indeed was foreordained before the foundation of the world, but was manifest in these last times for you" (I Peter 1:17-20).
Just as we know that once a law is enacted that someone will eventually break that law, God knew this as well. He also knew that it would be impossible for the law breakers to rescue themselves from the bondage of sin and so a plan for a Savior was made. Whether God knew that sin would enter immediately into the world with Adam and Eve, or just that it would bound to happen eventually, it doesn't change the outcome.