I believe there is a God, and I cannot prove it. If I could prove it, I would not need to believe.
Many believers in God think that they actually can prove it, although that "proof" may not amount to much of anything to anyone else.
I have a friend who claims to be an atheist (used to be a 7th day adventist, then a Scientologist) - and he claims he has proved there is no God.
Asked him how, and he said he stood on a hill and called out to the sky - "God, I do not believe in you. So, if you exist, then strike me dead right here and now". As he survived it, he congratulated himself on "proving" there is no God. He was serious. I did not comment, as I could not think of anything nice to say about this idiocy.
One of the definitions of agnosticism is that this person believes that the existence of God is in principle unprovable - either positively or negatively.