How can we explain high redshift numbers? I just finished an introductory astrophysics course$^1$ and I have a lingering question that I can't seem to resolve.

We learned that for the first few hundred million years, the universe was pretty boring and not much interesting$^2$ happened. We also learned, correctly or not, that the first stars started forming somewhere between 500 million and 600  million years after the Big Bang.

We also learned how to use redshift values to calculate age, and we talked about how the highest $z$-number we've discovered is some galaxy (GN-z11) at roughly $z=11$.

Using this calculator, we calcultaed that this galaxy apparently formed about 410 million years after the Big Bang.

So, this galaxy seems to be older than when astrophysicists think star formation happened. How can this possibly be? Clearly one of my assumptions is wrong, so is it:


Stars actually started forming before 500 million years post-Big Bang.
Using the UCLA calculator to calculate age is technically incorrect.
A galaxy doesn't need stars to be considered a galaxy.
Some other assumption I made is wrong which makes this post invalid.


As a follow-up question, what happens if we keep finding galaxies at higher $z$-numbers? At what point do we need to reconsider our theory about what happened in the "early" universe?



$^1$I'm not an astrophysics major, so forgive any blatant falsehoods in this post.

$^2$On a macro-scale, at least.
There is evidence that this assumption is incorrect.


  Stars actually started forming before 500 million years post-Big Bang.


There is some evidence that Population III stars formed as early as 200 million years after the Big Bang. The oldest known star, the Methuselah Star, dates back to 200 million years after the Big Bang. It is a second generation star (judging from its metal content), so that means a generation of very large stars must have lived and died before this one was born.