Let me ask you a question: You and I have never met -- so how do you know I even exist? The answer is obvious: You know I exist because you've seen enough evidence to convince you I exist -- perhaps a photograph, or a conversation with someone who has seen me.
And the same is true with God. We believe in Him because He has given us enough evidence to prove to us that He exists. In other words, He hasn't hidden Himself from us; instead, He has revealed Himself or made Himself known to us. God wants us to know Him -- and has done everything He needs to do to make this possible.
How has He done this? One way is through the physical world He created, with all of its beauty and complexity and wonder. Isn't it more logical to believe God created it than to believe it happened by chance? As the Bible says, "Since the creation of the world God's invisible qualities -- his eternal power and divine nature -- have been clearly seen, being understood from what has been made" (Romans 1:20).
But God has revealed Himself to us in an even greater way: by coming down to earth and taking on human flesh. That person was Jesus Christ. Do you want to know not only if God exists, but if He loves us? Look at Christ, for He came to demonstrate God's love for us by His death and resurrection. Don't remain filled with doubt, but turn to Christ and open your heart and life to Him.