We cannot deny the existence of God but accept the existence of evil. To call something evil means there must be something good to measure it by. God is good, whether or not we believe it or understand it. Ravi Zacharias says, in his book Jesus Among Other Gods:
"If evil exists, then one must assume that good exists in order to know the difference. If good exists, one must assume that a moral law exists by which to measure good and evil. But if a moral law exists, must not one posit an ultimate source of moral law, or at least an objective basis for a moral law? By an objective basis, I mean something that is transcendingly true at all times, regardless of whether I believe it or not."
We live surrounded with God's goodness. He is good to send the rain that nourishes the earth to bring forth the flowers of spring. He is good to give the birds a song and people ears to hear their singing. He is good to bring the new life of a baby and to use a mother to continue His creative work. He is good to show us mercy and grace and His abundant faithfulness in our times of doubt. God is good, whether or not we believe it or understand it.