A pillar of cosmology is the Cosmological Principle (Milne 1935) stating that the Universe approaches isotropy and homogeneity with increasing scales.
https://academic.oup.com/mnras/article/467/3/2787/2957031
I have to believe the universe is so much more vast than the farthest observable objects that our "bubble" of limited observations has to be less than a one in one-trillionth of Everything. There will always be more beyond.
What does that mean regarding the concept of a non-Copernican observer? Of course we are non-Copernacan observers. But, would the distribution of energy in a Big Bang formed universe over more than 13 billion years ago still be locally inconsistent to such an observable degree? Possibly.
However, it is also possible to misinterpret observations such as light shifts, which may not indicate changes in velocity where a momentary velocity is the only information the light shift can provide.
The Nobel Prize was awarded for research into the expansion rate of the Universe that brought two foundational concepts to the fore. One is the conclusion that our universe is accelerating in its expansion, and two, the addition of "Dark Energy" to explain that acceleration. Considering the cosmic scale and the idea of General Relativity bending space-time, the acceleration we observe in the expanding universe is probably not a result of any forces but the bending of space-time.
If we take that first Singularity as the ultimate gravitational well that bent all space and time back in to itself, all paths (geodesics) led inward. But, with the impossible explosion of that singularity, with its initial burst of energy to create the expanding universe, those inward leading geodesics unravel. The father out the universe expands, the less those inward geodesics point inward. Their affect on space-time would necessarily lead to a growing acceleration as they weaken and expand (time speeds up the farther from that central Singularity things get), making it look like the universe is under the influence of Dark Emergy, when it is really the shifting acceleration vectors of space and time itself.
Just a thought.
-Will