Maybe start with the fact that the universe is so finely tuned that if we changed the gravitational pull by 0.00000000000000000000000000000000000001% (37 zeros, no exaggeration) we would not exist. If the percentage of the elements were even altered at all, we would not exist. There are plenty of arguments for a designer with the teleological argument, these are just two.
Ah, the "fine tuning" argument. That's one of the more recent ones, true enough. Of course, as you already said, it assumes that there's only one universe which is why the multiverse idea is a threat to it. It's also a good sign that theists have given up on the ones that they used to use against evolution, as this one is about physics, not biology, and sort of relies on the idea that the universe is millions and millions of years old and not just 4,000 odd. (So it's hard to be a Bible literalist and believe in that one.)
So, the basic idea is that
(1) it's
fantastically unlikely that things should have been this way by chance, and
(2) therefore it wasn't by chance, and
(3) the only other way it could have been is if there was a designer God, who by coincidence is exactly the same one mentioned in a set of ancient Hebrew texts and not that guy Oden or Allah or any of those other fakers oh no.
Exactly how are we to know (1), though? If I know there is one red marble and 10 billion blue marbles in a bag, I know that it's fantastically unlikely that I will get the red marble. But what do we know about the possibilities of other universes? We're not in a position to know the probabilities. Also: if we think of time sort of Newtonian-ly, then there could've been an infinity of other universes before this one. And the possibility of getting even the most unlikely of universes in an infinite time is 100%. That's infinity for you!
Now, 3 assumes that if the universe didn't arise by chance then it must've arisen by the hand of [insert name of preferred deity here]. But if we're allowing evolution in a biological context (as most proponents of the fine tuning argument have conceded) then why not a variant of it in cosmology? Couldn't some kind of evolutionary procedure have produced our universe? I don't see that it's any less [edit: I mean MORE, of course] incredible than your Giant Ghost Man hypothesis.
Finally, as Hume pointed out, any "designer" hypothesis works like this: a certain thing is said to exhibit amazing complexity and thus to require explanation other than chance. Thus, a designer
complex enough to have come up with an idea of the complex entity in its head, and thus
far more complex than the thing it purports to explain is invoked. But clearly there is now an even greater puzzle to be solved: where did the designer come from? If the proponent of the design argument thinks that
that complexity doesn't need explaining, then why did the first kind?
