If astronomy is about the observation of the cosmos, often a picture "this is how the cosmos looks like" is presented. But this is not true. Stars that are only a few light-years away reflect a "relative" reality of observation because light takes only a few years to reach us. But light from the most distant galaxies, needs billions of years until it reaches us and can be detected by measuring instruments. In this time the real relations of the observed objects might have changed completely. Thus we see into a differentiated past of the cosmos, which contains little real, but much past.
Are there viable research approaches to this question that produce a more realistic picture of the evolving cosmos? How is this question dealt with in research?
The picture of the entire Universe emerges not only from observations, but also from models. We observe celestial objects in different stages of their development. From this, models can be derived about the development, which in turn are tested against the observations. Only from the totality of models and observations do we obtain an overall picture.
Most galaxies that are within a few million to a few tens of millions of light-years from us probably look almost the same now as what we see. There may be small differences due to the formation of new star clusters or the disruption of old ones, but their overall structure is not likely to be much different from what we see. The only exception to this is that if there are several galaxies relatively close together, they may have interacted with each other since the light by which we now see them left them; but such interactions take place over tens or hundreds of millions of years, so for such "nearby" galaxies, even that sort of change is unlikely.
Of course, looking at things hundreds of millions or billions of light-years away, odds are that the galaxies now look completely different; so what we gain from looking at such distant objects is not a knowledge of their present, but of their past. And THAT is the whole point of looking at such distant objects. We can't see what our galaxy looked like in the past, but if we can see what appear to be otherwise similar objects, they may show us how things have changed. In particular, it is hoped that with the JWST and later telescopes we may be able to find galaxies that (at the time the light we see them by left them) hadn't had time to form any stars that contained the heavier elements of which we and our planet are made. There are theories about how such stars produced elements beyond hydrogen and helium, and most of those theories are probably correct; but only a detailed study of gases ejected from such early stars can confirm or disprove those theories. Still, that's currently cutting-edge or even slightly beyond currently cutting-edge astronomy, so whether such studies will confirm or disprove current theories may not be known for a few decades. (Not that it makes any difference to the end result, since we're stuck with the elements we have here now, but at least it's not quite as esoteric as some other branches of science.)