Ignorance is not "questioning the the unquestionable". We have ways to measure the distance to things in space. They're not perfect, but they're not, as you suggest, useless either.
In other words, even background radiation and redshift are not provable as NOT being caused by, for instance, the surface of a bubble refracting light in a closed system. That would also explain why there is light going in every direction, aka "everything is moving away from each other" heat death religion.
That's not science, but guesswork built on basic assumptions that are not provable, it's all measurements in a void. If the universe was proven to be a closed system, all that science and your whole cosmology goes in the bin.
We got models. They work pretty good as far as we can measure. That some other model could potentially explain the same measurements doesn't change that fact.
If someone proposes some other model that explains something better, ie with same or better accuracy and/or with less assumptions, then great!
Occam's Razors says your cosmology is wrong. It's too convoluted, it has to explain the craziest singularities, which are not observable, yet it cannot explain real observations, like missing energy sources and background radiation. No math changes these facts. It's all in your head.