It seems that God does not exist; because if one of two contraries be infinite, the other would be altogether destroyed. But the word "God" means that He is infinite goodness. If, therefore, God existed, there would be no evil discoverable; but there is evil in the world. Therefore God does not exist.
-- As Augustine says (Enchiridion xi): "Since God is the highest good, He would not allow any evil to exist in His works, unless His omnipotence and goodness were such as to bring good even out of evil." This is part of the infinite goodness of God, that He should allow evil to exist, and out of it produce good.
Summa Theologiae 3.1.3 ad 3:
But there is no reason why human nature should not have been raised to something greater after sin. For God allows evils to happen in order to bring a greater good therefrom; hence it is written (Romans 5:20): "Where sin abounded, grace did more abound." Hence, too, in the blessing of the Paschal candle, we say: "O happy fault, that merited such and so great a Redeemer!"