Vlad,
Either it has an external creator,…
Do you remember the episode of Porridge where Fletcher was in hospital and Mr McKay was desperate to know what they’d done with the earth they’d excavated from a failed tunnel? Fletcher said he’d tell him in in exchange for a bottle of scotch. Mckay agreed and gave him the scotch. Fletcher called him close and said, “Well Mr McKay, the truth is we dug another tunnel and put the soil in there…”.
That’s the “external creator” argument. It just transfers the same questions about a naturalistic universe to a supernatural creator of the universe.
…it has been around forever (although we would need an actual infinity rather than 'the maths'…
Could be, though “forever" is probably meaningless because it fails to take account to the possible nature of time – looping for example.
…or it popped out of nothing.
That’s incoherent. Various of the competing hypotheses don’t require that (whatever it means) because they posit plausible alternatives – quantum borrowing for one.
Short version: your three possible options are naïve and folkloric, failing to take into account various, better reasoned options
In interview with Robert Kuhn Sean Carroll was asked this question and seems to end up admitting there could have been nothing but we have a contingent universe depending on...…...luck.
Sounds right to me. Luck is identified by the person who thinks he’s been lucky. We may think we were lucky because "the universe" produced us. A differently organised universe could though have produced a different (though equally not very bright) person that thought “he” was lucky that the universe was just right for him to appear etc. Inferring something remarkable because the universe produced us is just the old reference point error (also known as the lottery winner’s fallacy). For what it’s worth I agree with Carroll if what he was saying was that the universe neither knew nor cared what species, if any, it would produce. Why would it?