A young student grows up in a society that holds the belief where she, like everything else, is made up of tiny unseen particles called atoms. So after learning something about the methodologies of science, she decides to understand what the science is behind the atom.
What strikes her at first is how the explanations for the atom didn't fit at all into the scientific method, but relied heavily on everyday experience. Furthermore, no modern physicists have witnessed such experiences, but rely solely on the accounts of early physicists. Some physicists claimed to have experiences that tangentially supported the experiences of the original physicists, but none of them could produce any evidence remotely like that which holds for other theories.
Upon further investigation, she realises that physicists disagree among themselves as to which experiences count as evidence of the atom. Some physicists argue that the experiences are interpreted too literally, while others hold to as literal a reading as possible. Some argue that the experiences can only be understood in light of arcane mystic writings and ancient mythic tales, and there is disagreement among those physicists as to the process this takes.
The quality of evidence is further called into question when other physical theories adequately account for the evidence for atoms without needing to posit atomic theory. She finds physicists will admit this in parts, but again there is disagreement between physicists over which scientific phenomena explain away the need for atoms in any given case. Some physicists spoke of the atom in metaphor, some shrouded knowledge of atoms in mystery, and some asserted that certain experiences of atoms were brute facts.
But not all physicists even agreed that evidence was important. Some physicists argued from first principles alone, invoking philosophical arguments that spoke of the atom's necessity in some respect. There were multiple of these arguments, though physicists disagreed among themselves as to the validity and significance of various arguments. Entire classes of arguments were championed by some physicists, while others favoured a different kind of arguments. She found the arguments for the most part lacking in any detail, and where there was detail it contradicted other established science. There was just no way to reconcile the arguments with the claims made about atoms.
She found some physicists who disagreed with both the arguments and the evidential approach. Some argued for the beauty of the idea as proof of the reality of atoms. Other physicists argued that atoms fit with our emotional needs. Some argued that the atoms were needed to keep social order. Some argued that their emotional response to the theory is its proof. Finally, some physicists admitted that a belief in atoms is a matter of faith, which a few embracing the idea of atoms precisely because they are an absurd concept.
The only constant she found in the exercise was the belief itself. Physicists couldn't decide among themselves what the implications were, let alone any detail that could be subject to the same scrutiny that other physical theories have. What follows is that the consensus among physicists is an artificial one, with no two physicist sharing quite the same view of what an atom is or how we know about it. And, finally, the reasons and evidence given in favour of atomic theory were unlike the various successful epistemologies that she had learnt about. At that point, there was nothing to do for the idea of atoms than to just walk away until such time the concept became more scientific... though she doubts that would ever be the case.
The question "does God exist?" has been the focus of more than enough academic inquiry that the inquiry itself deserves to be taken seriously. In any given field, outsiders looking in are looking at the promise of a discipline to be able to provide satisfactory answers on the questions it purports to cover. This isn't always easy, as academic discourse tends to become self-sustaining making it harder for outsiders to be able to make sense of it. So some latitude must be given for outsiders simply not to "get it" when it comes to the validity of the questions and the approach to answers the discipline offers.
Two things to recognise are that a) no human endeavour is truly in isolation, and b) there are a lot of ways to spend a lot of time asking wrong questions. Astrology and alchemy good examples of both. The methods of astrologers and alchemists throughout the ages have overlap with the methods used in science and philosophy. And both astrology and alchemy are nonsense notions that had a lot of ink spilled over a long time by some very smart and learned people. Very few of us are astrologers today, and none are alchemists, yet as outsiders we feel sufficiently qualified to write off both intellectual disciplines as failed truth-telling endeavours about the universe. It could have turned out both were true. It turned out neither were.
What I tried to do in the parable above was highlight my own experiences trying to understand the question of God as believers see it, including what philosophers and theologians have said about the question. I grant the possibility that there could be a theologian out there who has a legitimate case for God's existence, but I don't see the worth of exploring the subject in any great detail. Despite the towering intellects and sheer amount of manpower thrown at the problem, there doesn't seem to be the same conversation among learned believers about what God is and does - let alone a case made with the successful epistemologies we have developed. This stands out in contrast to the actual atomic theory - or any other scientific theory - where the scientists have general agreement as to what theories are and the state of the evidence, even if they sometimes disagree on detail.