Whether or not you believe in God, you can understand the concept of an omnipotent God who runs the universe the way that he wants to. Why shouldn't evil exist if God feels that it serves a purpose in the world? Again, you don't necessarily have to be a believer to see how the two concepts fit together.
"God" (which I will be using to mean ANY supreme being) and "evil" are simply names given to help us understand the basic workings of the universe. "God has a plan!" And this is good to remember, because the Universe DOES have a plan and humanity is only the tiniest fraction of that grand design. Bad things happen because life is not black and white, it is fluid and dynamic. God is the positive and evil is the negative and both poles need to exist for the Universe to function.
Yes, I think it is possible for God and real evil to be reconciled. However, this is totally contingent on the real evil. God is all loving and never at odds with anyone. The real evil would have to ask for forgiveness and God would surely grant forgiveness to the real evil.
Weighing God and weighing evil, one will not find an auditor's balance sheet. The God knowing person however, knows one thing: God is beyond our knowing. The God who created this cosmos in which we all live and breathe and have our being can no more be held accountable to an auditor's inspection than my child can pass judgment on what I make for supper this evening. In the religious literature assembled since humans learned to write, we learn of God's greatness so beyond our own and we are encouraged to carry a grateful heart into understanding the horrors we encounter. With that grateful heart we will know the power of the Holy One to accompany each created one through every evil moment building an unbelievable strength and courage that gives life to all creation.
I do not believe that God and real evil could be reconciled. God is what people believe to be the supreme ruler, of everything good and just in this world. Real evil is the exact opposite of that, those who are truly evil would not want to reconcile or wish to change.