I know God exists because I have seen evidence of his existence in my own life, as well as in physical manifestations in the world around my by way of undeniable miracles.
I personally witnessed the following:
A woman in my church had most of the vertebrae in her back fused together after a horseback riding injury, she couldn't bend her back and was always in pain. We all gathered around and prayed for her, the pain left, and she was able to touch her toes, something she hadn't done in over 20 years. X-rays confirmed that the fused vertebrae were no longer fused.
A friend of mine had torn a ligament in his hand (the one connecting to his thumb) right off the bone, and had no control over his thumb. He needed surgery to fix it, and the doctors only expected 40% total movement & control to return after the surgery. He was at a healing conference and raised his hand when they asked for people with hand issues, we heard a pop come from his hand, and he was immediately able to move it 100%. His doctor, formerly an athiest, now attends my friends church.
I was in a pretty bad car accident that damaged several ligaments in my back, and required physical therapy. My Doctor even debated surgery, but then deemed it not necessary. I was in serious daily pain and on pain medication/muscle relaxers right up until the day I got prayer from the congregation at my church. Since that moment, my back pain left, I went off all medication, received no more physical therapy, and my doctor said the injury was completely gone. In addition to this, a genetic curvature of my spine that concerned my doctor went away as well.
Heard from reputable sources (personal friends):
On recent mission trips to Africa & Honduras, a good friend of mine saw the following, corroborated by several witnesses:
AT LEAST 5 deaf people regained their hearing. 2 Blind people regained sight. A girl with severe autism completely healed an socially normal after prayer. A young man healed of cataracts, they watched the cloudiness disappear from both eyes. 2 Women healed of hernias.
In Uganda, one of the former leaders of a rebel group responsible for killing multiple thousands of people (The LRA) was recently saved. He left the group and now travels preaching the love and peace of Jesus. Several friends of mine were there to see him speak to a group of villagers whom he was responsible for many deaths of family members. He expressed his deep sorrow and shared his testimony.
These are just a few things I've seen or heard recently. Just because you haven't seen the evidence of God's power does not mean it doesn't exist. I have personally witnessed many undeniable examples of the power of God being displayed in the physical world. I am not engaging in blind faith, but in an active, living relationship with a loving God that I don't believe exists, I KNOW He exists.