How to Settle the Burden of Proof

I want you to picture a guy, let's call him Paul, walking into an urban police-station. Beaming, he proclaims that he knows what happened to the dead body that was found in the river five days ago; that he's solved the mystery.

Let's assume that by some random chance, or maybe out of desperation, the police actually take him seriously. So they ask him in, lead him into a room, sharpen their pencils, switch on the tape-recorder, and take a statement. This is how it goes:

PAUL: "You ready? Can I start?"
OFFICER: "Sure. Please tell us what you know."
PAUL: "You see, he was murdered. Frank did it."
OFFICER: "Frank... Frank who?"
PAUL: "Well, Frank of course. Frank Frank. Who else would I mean?"
OFFICER: "..."
PAUL: "..."
OFFICER (With disappointment at the realization that this won't be the clue they'd been hoping for): "That's it? That's what you came to tell us?"
PAUL (Genuinely puzzled): "What do you mean? I told you what happened. What more could you want?"

We could imagine this going on indefinitely, but this little conversation is enough to illustrate my point. Merely tossing a name out there and proclaiming that a murder took place is not the same as truly solving the mystery of an unidentified body.
Yet, this is exactly how religious people tackle the question about the origin of our universe. They proclaim that it was "made", and that it was "God" who made it. And then they lean back, satisfied with their accomplishment of having "solved" the mystery, gaze us a beaming smile, and react confused when we reject their "explanation" as preposterous and stupid.

To complete the analogy, let's have Paul defend his thesis by proclaiming that it's more likely Frank committed a murder than that the water of the river simply morphed into a dead body.
This is analogous to the claim frequently made by theists that, due to the apparent fine-tuning of our universe, it being made is more likely than it just coming into existence "by a giant explosion". Of course, nobody ever said that a giant explosion was the origin of the universe, just like nobody at the police-department proposed that the body is actually magically transformed water of the river.
The Big Bang Theory is actually not about the origin of the universe: Like the police, we're still pretty clueless regarding that mystery; like the police, it's likely we'll solve it eventually. What the Big Bang Theory actually is about is the early development of the universe: The theory states that the universe transformed from a very hot, very dense state to a less hot, less dense state, which is analogous to the police stating that it's very likely the case that the body they found was, at some point in the past, alive. It's something we know beyond reasonable doubt. It's something we can prove pretty much for sure.

There are tons of people like Paul out there; People who really do not see the problem with the sort of oversimplified skyhook-explanation they give for complex problems. They are ubiquitous, and while they tend to be annoying, their existence does not actually bother me.

What does bother me is that my analogy fails in one very important point: Paul the potential witness is regarded as a lunatic by society, and will probably find himself in a mental institution in the near future. Paul the theologean, on the other hand, is a highly respected member of society, gets invited by TV-stations to comment on enormously important political topics and has a huge influence on public opinion regarding an incredible variety of topics.