The cosmic background radiation (CMB) is estimated to be from 13.7 billion years ago (BYA), and very shortly after the big bang compared to that time frame. The oldest coherent objects we've detected are around 500 million years after the big bang, making them 13.2 BYA.
If I understand these stories correctly, that means that we have not yet detected any radiation that can be clearly identified to be emitted from a source between these two times (otherwise NASA would announce an even older discovery). I don't think that that is implying that there's nothing there to see, although it's obviously the case that it is beyond our current technology to see in that window. The severe redshift and small solid angle are two complicating factors, another is that most galaxies were only beginning to for around 13.2 BYA.
Regarding astronomical objects of ages between 13.2 and 13.7 BYA:
- What is there to see? Obviously, the 13.7 BYA point has the problem of near homogeneity but what about the times in-between? Are there cosmic structures that we could see there but no where else? Things that predate proto-galaxies? After the CMB, did matter stop radiating? Are there other near homogenous emissions we could look for? Does that make any sense? What is an accurate characterization of that time frame? Does physics make good predictions for astronomers to chase? What discoveries in that time frame are next?
- What telescopes will see them? The record holding earliest protogalaxies I reference are highly red-shifted light and the CMB is $cm$ wavelength. Would new discoveries in this time frame mostly be in-between those two wavelengths? Are there promising telescopes that might open up new areas of study here?