You claim that God doesn't exist because there is evil in the universe and If God is there, there should be no evil.
God is there why? because we are there, because the whole universe is there. It's impossible to assume that all that universe happen by chance. It's against the common sense.
One thing can convince any human being that there is no God which is to convince him that there is no universe and he himself is not there. Or to convince him that the universe is created by chance which happened once to create the earth and happened again to create our father Adam and then again and again to create Eve. Does it make any sense to you?
But if God is there and is telling us that He is Pure, Good, Loving and Fair?
If so, then where does evil, hatred and injustice come from?
God tells us the life we are in here is a test. He has created everything existing and He created whatever happens as well. There is nothing in this existence except what He has created. He also says He created evil (although He is not evil). He is using this as one of the many tests for us.
Consider people who do so much evil in the earth and then live to a ripe old age in the splendor and wealth of their ill-gotten gains and die without ever being taken to task for their deeds. Where is the justice or fairness in this?
Believing in one God and in the day of judgment when all people will be judged, make me feel peaceful and able to answer many questions.