No question troubles the minds of thoughtful people more than, “If God is good, why is there so much suffering in the world?” I’m not surprised that you struggle whit that. There is no one–no one!–who stands by the bedside watching a loved one die from cancer or who sees the terrible shooting in Tucson or who reads about human trafficking or who hears about thousands killed in a tsunami who does not wonder, “Where is God in all of this?”
There are many ways to answer the question, and many of the answers are very good. Certainly we can say that the world is the way it is because of the catastrophic results of sin. Because Adam sinned, death and destruction entered our world (Romans 5:12). Now the whole creation groans (Romans 8:21-23), waiting for the day of redemption. So one way to say it is that the world is the it is because e are the way we are.
Then there is the answer of God’s sovereignty, which tells us that God himself is involved in all that happens in this world. As Tony Evans has pointed out, everything that happens in the world is either caused by God or allowed by God, and there is no third category.
To ask, “Why did God allow the holocaust?” is a subset of a larger question, “Why did God allow sin in the first place?” Though the Bible does not answer this fully, we can say with confidence that God allowed the entrance of sin so that his glory might be seen in the forgiveness of sin and in the restoration of the universe to what it was intended to be.
As far as believing goes, your starting point is all-important. If you start with tragedy, it will be almost impossible to reason your way back to God. If you start with God, you have at least started in the right place.
See Why is there so much suffering in the world?