Thinking about how both God & evil can coexist … given this proposed dichotomy: "God can either do literally anything and everything, or he cannot":

If God can do literally anything and everything, this includes things that are contradictory. Ex, he can make a square circle, or can create something the smells purple. If this is so, there is no problem with God's goodness and the existence of evil in the world, because since God can do anything, such seeming contradictions should not faze us.

On the other hand, if God cannot do literally anything and everything (as is suggested in the Bible, ex God cannot lie), then this means that there are certain things that God cannot do. Thus, it is at least possible that the existence of free-willed creations (which could freely choose evil) and God's omnibenevolence (perfect goodness) and omnipotence (all-powerfulness) are not incompatible, since it may not be possible for God to have the former (free will) without the latter (evil) to some degree.

This is part of the argument given in Alvin Plantinga's landmark (but difficult since it's written for philosophers) book God, Freedom and Evil … at least, as I understand it. (Short essay based on the book is available here.) He goes into considerably more detail in that book and no doubt with much more precise terminology and philosophical acumen than I have here. Not sure why it suddenly came to mind today, but thought I'd type it out. It makes sense in my own head …