Yes, God exists. When you have had a rare cancer, and survived, you know there is a God. When I found out I had cancer (Merkel cell carcinoma), and had to have surgery, radiation, and chemotherapy, the first think I did was pray to God to let me survive it.
I prayed to him to please get it out of my body. When something like this happens to you, you don't think "Mom, I hope I make it", or "Dad, get this cancer out of me". Sure, they are the most important people "in" your life, but you also need to remember God. I wasn't praying to an "energy", or "science", I was praying simply to God. He can be my God, your God, or someone else's God.
I was also almost lost in a forest once,while backpacking with 1 friend. All of a sudden, I realized I was alone, and panicked because my friend was not answering me, and I could not find him. Again, the first thing I did was ask God to help me find my friend. I soon found him.
Even with simple things there is God. I recently needed to pass an exam at my job, to be able to advance. I took the exam. By the end of the exam, I wasn't really positive if I passed. I went to the restroom, and on the way back, I again asked God to help me. "Please, God" let me pass this exam. I did.
These example prove to me there is a God. They may not prove anything to you, but it doesn't matter. Everyone needs to find out for themselves, if there is a God for them. I just hope there is a God for you, when you really need him, like I did.
Frank