How Can a Star Be Older Than the Universe?

It wants to be the answer, yet the facts don't really align with the premise of the question. We just shoe horn a litter of observations into some post-hoc rationale for how the universe "began" and then we retcon anything that doesn't make sense, when we think more deeply about it.

It's fine to have cosmic background radiation, and elemental distributions and ratios, and sure that all kind of lines up, pointing to some large, highly influential event in the past.

But just because we can chart certain facts doesn't mean the story stops where our charts end.

I'll concede that something really important happened 13-ish billion years ago, and that it represents a significant temporal horizon, beyond which we cannot draw conclusions, yet because we cannot see beyond the peaks of some mountain range does not mean the edge of the world resides on the other side.

All the mental backflips required to rationalize The Big Bang, and then from the other side of your mouth, murmur that it actually wasn't a "bang" but instead an "expansion" really just result in a colossal defrocking of the theory.

  Hey look guys, here comes
  emperor Big Bang in his
  super comfy new clothes!

And if it seems that we don't really know what was going on, as we try to recreate a march back inward to the hypothetical origin singularity, and every time we try to walk events backward, they stop making sense, we just need to say we don't really know.

The Big Bang is a smelly theory, and it smells wrong. There's a lot of evidence of a really powerful event some 13 billion years ago, and it may have been transformative, but there's no basis to the claim that it was truly event zero.

Just as possible is that we're the fallout of some localized very large bang, that cleared out a radius of space time that is more distant than we can observe. This idea is not interchangeable with the big bang origin story of the universe. It's not an Occam's razor victory in favor of the big bang.

If we are stuck within a spatial temporal crater as the result of a non-unique very large bang, it would mean that we can look differently at how we model the bang, and come up with saner conclusions than "oh, it just popped into existence, and then went kablooey, and that's okay because the very idea of time is bound to that ever even happening at all."

Like, sorry, that hand wavey whitewash doesn't adequately paper over the possibility of retconning some nonsense into the narrative, because it would be a threat to academic authority to say "we don't know" regarding the nature of a hypothetical origin singularity.

I get that there's no evidence beyond the reaches of our deepest observations, but it's lazy to put forward that because we can't grasp at evidence beyond certain terrestrial limits, then we get to say that we know conclusively that the observable limits are known to be the actual limits and thus the assured origin of all space time.

What we should say is that there is a depth beyond which we cannot summon further evidence, and while there seems to be some tumultuous event back there, we don't know what happens prior to that or where that limit comes from.

Because we really don't know.

I'm presuming this is happening at some non-trivial relative velocity on the grounds that it's hardly a "big bang" if it's actually in the same velocity vector as the location in which it occurs, and doesn't have any new material coming out.

You're kind of overextrapolating the "we know nothing about pre-Big Bang conditions" based on the English phrasing of a more mathematical idea. We can eliminate some things, like as we are discussing, the possibility that the Big Bang occurred in an already-existing universe in some way that it could create a visibly older star showing up a mere 100-200 light years from us. I can't eliminate the possibility that there's some "collision" happening out of our past light cone, or that a Big Bang occurred and that taking into account metrics of space this time, that it simply "blew" all the old universe out of our past light cone as our universe inflated. But I can eliminate the idea of some older universe being something we could co-exist in local space with. It would produce visibly obvious results that we do not see, a fairly violent cataclysm that would have results that we could see. As we parse the Cosmic Microwave Background, we're parsing twitches and fluctuations far, far smaller than such an event would have created. This would be writ large on the sky, not something that could sneakily inject a star into our galaxy that we only notice after hundreds of years of astronomical observations.

We can't make very many positive assertions about pre-Big-Bang conditions, but we can make a few negative ones like this.

I'd also point out it's not an intrinsically crazy idea. Some variants of String Theory hypothesize situations in which it would be possible for a "Big Bang" to occur in an existing universe like ours, due to membrane collisions. It could well have happened elsewhere. It just doesn't seem to have happened in our past lightcone.

They mention that the current universe age fits "within the bars", for example but also mention arguments for universe being younger as well, which would again put the measurements at odds.

Basically, both of these values involve a string of assumptions and while getting every single one of them to high accuracy is a remarkable achievement, the chance of some glitch in either measurement is significant.

At first glance, the distance of 32 billion light-years (9.8 billion parsecs) might seem impossibly far away in a Universe that is only 13.8 billion (short scale) years old, where a light-year is the distance light travels in a year, and where nothing can travel faster than the speed of light. However, because of the expansion of the universe, the distance of 2.66 billion light-years between GN-z11 and the Milky Way at the time when the light was emitted increased by a factor of (z+1)=12.1 to a distance of 32.2 billion light-years during the 13.4 billion years it has taken the light to reach us.

[1] https://en.wikipedia.org/wiki/GN-z11#Notes