Almost any concept regarding the origin of the universe is unintuitive. Can something come from nothing? No one intuitively thinks this, it makes no sense. Could the universe have no beginning, and always just existed? I don't think this makes intuitive sense to us either, the notion that there wasn't a beginning and that the universe extends forever into the past.
Same for god. How could a being simply always exist and never have a beginning? We can comprehend the notion of something existing forever into the future, once it has begun. We cannot comprehend the notion of something existing forever into the past, with no beginning.
And yet, here we are. Something (or many things) that is unintuitive to us has to be the case, because the universe exists and we exist. If we give more weight to one of the options without any logical reason to, then we might end up ignoring or rejecting information that gives us reason to assume the other options are possible. Wanting god to be real isn't a path to discovering god, it's a path to inventing him.