I want to assure you that God not only exists, but He also cares deeply about us. And He not only wants us to believe in Him but also to come to know Him as our friend -- both now and forever.
But something has happened that has cut us off from God -- and that "something" is sin. If God didn't exist, or if He were just a vague, impersonal force (like gravity), then sin wouldn't be a problem. But sin is a problem; in fact, it's our greatest problem. God is holy and pure, and every sin is an act of rebellion that cuts us off from Him. The Bible says, "Your eyes are too pure to look on evil; you cannot tolerate wrong" (Habakkuk 1:13).
How do I know this? I know it first of all because down inside, we all feel guilty. Why would we feel guilty if we didn't realize we'd sinned? But I know it most of all because of Jesus Christ. He came down from heaven for one reason: to become the perfect and final sacrifice for our sins. He didn't come to earth just to show us how to live; He also came to bridge the gap between us and God, by making our forgiveness possible.
The greatest discovery you'll ever make is that God loves you and wants you to be part of His family forever. And this can happen, as you turn by faith to Jesus Christ and commit your life to Him. Life without Him is a dead-end road -- but life with Him leads to hope and peace.