From what you say, I think the opposite is true; I don't think you're cut out to be an unbeliever!
Why do I say this? The reason is because I sense that in your heart you really want to believe in God and know Him in a personal way, which is the first step in actually discovering Him. Someone who doesn't ever think about God or care about God will probably stay that way the rest of their life, but not you. I hope you'll take seriously Jesus' promise: "Ask and it will be given to you; seek and you will find; knock and the door will be opened to you" (Matthew 7:7).
Like you, I too wonder sometimes why God allows evil things to go on in the world. But the Bible tells us two important truths that I hope you'll take seriously. First, it tells us that God has already done something about the evil in the world. When Jesus Christ gave His life for us and then rose from the dead, He confronted all the forces of sin and death and Hell and He conquered them. We have hope, because of Him.
Second, the Bible assures us that some day Christ will come again, and when He does, all the evils of this world will be destroyed. In the meantime, He wants to use us to overcome this world's miseries. I invite you to look at Jesus Christ as He is found in the pages of the Gospels, and then by faith to give your life to Him.