A question that I think fundamentally underlies the one “Does God exist?" is “Do supernatural things exist”? Obviously, an omnipotent God would be supernatural.
So, to start out I will say this: science cannot disprove the supernatural. Science is the study of things that act in predictable, natural ways. However, the supernatural is not predictable. If God exists, He would be able to appear in any way, shape, or form, and do any kind of thing, with no way to predict it. So, science can neither prove or disprove the supernatural.
The truth is supernatural things are present in the world. You may say “but science hasn’t documented it”, but it can’t. I will give a few stories that seem to show supernatural happenings.
First, a small first-hand story. I was at a retreat a year ago with my church’s (an Assembly of God) youth group. I had a migraine. Anyone who gets migraines knows they are not fun- they give you terrible headaches and nausea. I was sitting in the worship room in the evening service, but I just not feeling good enough to join in. A friend (not too close, more like an acquaintance) came over to me and asked what’s up, why am I not worshipping (because I usually worship fervently). I told him my problem, and he calmly put his hand on my head and said a quick prayer, which I didn’t even hear (modern youth worship music is loud. After he said “amen” and left, my headache was gone. No natural explanation is possible for that.
Also, the speaker there (Allen Griffin) told this story (can’t remember if it was before or after the previous). He was at an event one time, and he has this tradition of pouring small amounts of olive oil on the heads of participants. Well, one girl was there who had recently broken her neck, without paralysis, and was wearing a neck brace. When the oil was poured on her, she got frantic, started running around the building, and tried to take the brace off. Now, the speaker didn’t intend to do anything, and was rather worried about a girl with a broken neck taking her brace off. However, when she took it off, her neck was healed! And it was nowhere near the expected time for it to naturally heal.
A third story (one I almost witnessed) happened at my youth group one Wednesday night. Shortly after youth group ended, and I had left, people started praying over a demon-possessed teen. People who approached him, even without being told what was going on, describe a presence of evil. One described it as “going through a wall”. He was writhing and speaking in strange voices and languages. After a few hours, the demons left. Now, the church did not make a big deal out of this- I only heard about it in my teen Sunday School, not in service. A few weeks later the guy that invited that kid to service on Wednesday gave a brief testimony on what God has been doing in his life, with a short, passing statement that he had been freed from a demon.
How can science and naturalism explain all of this?