The CMB is everywhere, but it was emitted by the initial formation of neutral hydrogen (from plasma) in the early universe. When people talk about the CMB being far away they're really talking about the last scattering surface, which is that early plasma as seen 13+ billion years later.
CMB is produced by atoms, right? We see darker/lighter regions in CMB, so we should see a transition somewhere. 300M years is very short period of time, unless everything cooled very very uniformly, which is not the case. Sometimes, somewhere there must be a galaxy past CMB.
> 300M years is very short period of time, unless everything cooled very very uniformly, which is not the case
~300M years is the time between the Big Bang singularity and the CMB, but not really relevant. The entire universe was everywhere as hot as the surface of a star at the time of the CMB, so any evidence of galaxies forming before that is surprising.
The surprisingly high uniformity of the temperature of the CMB — isotropic to roughly one part in 100,000 — is one of the reasons the Big Bang model replaced one of the older competing hypotheses (continuous creation IIRC).
So it is in fact the case that everything cooled very very uniformly and I'm not sure why you think otherwise?
I'm also not clear what you're saying with
> so we should see a transition somewhere
Given the CMB is itself the transition that we see.
> Sometimes, somewhere there must be a galaxy past CMB.
I think here you're mixing up space and time.
It's reasonable (please permit my use of conventional language rather than 4-vectors) to assume that a galaxy exists on the other side in space of the CMB as we see it now, but that happens at a point in time after the recombination epoch began and space became transparent, and light from that event hasn't reached us yet; when it does, the apparent distance of the CMB will be large enough for the galaxy to appear on this side.
Are you familiar with light cones and the convention of one space axis and one time axis? It might help you visualise it if you draw what's going on.
GLASS-z12 is 33.2Bly away from us. It should be behind some of the CMB produced by BB, isn't?
> Given the CMB is itself the transition that we see.
In BB model, CMB emitted by hot plasma. Where it is, that plasma?
In steady universe model, CMB is light with z=1000, emitted by distant galaxies, in range of 4Tly. It explains high uniformity of temperature. It's like the temperature of a water stream from underground: it's uniform across a climate area because underground temperature averages seasonal temperature shifting.
The latter is what we're talking about when we say the CMB is about 13-point-whatever billion years old.
The difference with the other number is that the universe got bigger in the meantime, and that's where we recon it is now.
> Where it is, that plasma
The plasma itself?
Everywhere. The whole universe, including here.
The bit we see?
An echo made of light emitted at the last moment in time that it stopped being plasma — the light from the plasma that was here is now as far away from us as the plasma that caused the light we can see.
You have to be careful with what you mean by "distance" at cosmic scales. Space is expanding with time, and there are several different definitions of "distance" that give very different results at cosmic scales.
The best "distance" measure here is simply redshift. GLASS-z12 is at redshift z=12, as the name suggests. The CMB is at redshift z=1100, so it's father away.
In fact, for very straightforward physical reasons, no light can reach us from beyond the CMB. The universe was opaque before the time of the CMB, because it was ionized and dense. Before the CMB time, photons could not travel very far at all before they hit an electron and were scattered.
> Sometimes, somewhere there must be a galaxy past CMB.
If there is we'd have to wait for the light from it to get to us, by which time the CMB will have receded further and it would then be in front of the CMB.
A transition from plasma to the cold mater in the form of galaxies we see.
> Why not?
As you see, there are big clusters everywhere. It means that some regions were cooler from the start, to form these cluster in so short period of time. It means that regions around them were hotter, thus they should emit light longer.
> If there is we'd have to wait for the light from it to get to us, by which time the CMB will have receded further and it would then be in front of the CMB.
300My is a short period of time. Why they cannot sometimes overlap?