One reason, and probably the main reason why God doesn't exist [in the mind of the questioner] is that, if God really existed, He wouldn't allow all the suffering that is going on in the world, especially the raping and molesting of children.
He asks two questions:
1 - Why does God allow the raping and molesting of children?
2 - Can it be proven that God exists?
Understanding the Great Controversy Issues helps answer these questions.
However, that too, takes faith.
Can we prove that a great controversy is taking place?
Can we prove that a loving God has been challenged by a powerful rebel?
Did you know that a large section in the "novel" aisle of a bookstore deal with the great controversy issue?
I've not read any of the books but looked at the summary on the back covers. The major themes in most of these books is a "reversed" Great controversy story. (Reversed in that the saving Prince is seen as the enemy, while the dragonic prince is seen as defending life in present state. It's usually about a powerful prince and his associates trying to keep the earth or his kingdom from a prince who will invade and ultimately destroy dragon prince and everything on the earth.
However, that Prince that is coming, is the GOOD Prince Who will save us , the dragon prince is the originator and contributor and agitator to earth's suffering and problems.
Once that is established and the idea that God is allowing the rebel to show the true colors of his seemingly pleasing to self methods, then the reason for all the pain and suffering becomes apparent. God has allowed the freedom of choice to people that they might demonstrate the consequences of their choices and see the dreadfulness of sin, and in contrast the peace in even trouble of the righteous.
Sin is cruel. The sinful course of people in power leads even the innocent to suffer.
The evidence of God's presense is seen in the times when He does protect and make ways of escape for His praying people, or gives them the strength to endure.
Another great way to show that God exists is to point to the fulfilled prophecies in scripture. Prophecies that were written many years prior to their fulfilment.
Look at Daniel 2.
The message stands out clear --- the fake religious advisors couldn't come up with the correct revelation.
But Daniel connected with the REAL GOD and he was able to show and explain the kings' dream.
Further more that dream of the successive empires stands as a monument that God does exist and has accurate information concerning the future.
Finally, prophecy pictures things as getting far worse (great time of trouble) before Christ's coming. The powers of evil will be allowed to make a final display of their form of government.
If we think nothing bad ever should happen because God is love, we dont' understand the issues.