Sifos, you yourself said you can't prove that something doesn't exist so I think we agree you can only increase your confidence that God does not exist and never actually say with complete certainty that He does not. You may consider it improbable that something does not exist and maybe since you have never seen an orc, elf or unicorn you are inclined to believe they do not exist. While it is of course impossible to say they do not exist, it is rational to assume they do not due to the rules they are "known" to follow (e.g. they would theoretically have material representation and be of such a size that they would be readily visible). God is a self-consistent immaterial being/force that by the very "rules" ascribed to Him are non-observable. God does serve to answer questions about the universe that are currently, otherwise, unanswerable (e.g. the existence of energy and matter - the existence of universe... God is of course the self-consistent answer that God has always existed).

If the laws of conservation of matter and energy are ever broken then there would be a lot more ground for rational atheism but as things stand you can't see God and you shouldn't be able to and He/religion is currently the only explanation for existence. I do not think it makes sense to put your faith in violation of the laws of conservation of matter and energy to try and find some reason for existence.