There were no objects before the CMBR. The universe was so hot that atoms couldn't even form. Once it cooled to the point where hydrogen atoms came into existence, the CMBR became possible. I'm talking at the limits of my knowledge, so allow me to refer you to this video by Fermilab that's pretty good.
I think OP's question related to the observable universe vs what is beyond. We see the CMB (and thus our limit of light) only to a point, but that doesn't mean there's nothing beyond that - otherwise we'd be the literal center of the universe (I recall an old minutephysics video[0] on this).
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.
> 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.