Red shift theory is precisely the problem with Big Bang cosmology.
Astrophysicist Halton Arp has written excellent books about this.
In a nutshell, the assumption that red shift relates totally to relative velocity has been refuted. This in turn refutes the whole cosmology of the 20th century, including Big Bang, Dark Matter etc.
For that matter, Dark Matter was essentially refuted by the famous Higgs boson experiments at the Large Hadron Collider at CERN. These experiments covered the energy ranges where evidence of Dark Matter was expected by theory, and NOTHING WAS FOUND.
Of course, this is not a headline, because it collapses the whole edifice of Big Bang cosmology.
For those who may not know: Dark Matter is nothing but a FUDGE FACTOR to make the General Relativistic equations comply with the ASSUMED BIG BANG Universe.
Physics is in for a MAJOR EMBARRASSMENT, sooner or later, over the whole BIG BANG FIASCO.
What part of the cosmology?
Remember that the atheists believed in a universe that always existed, and red shift (which is not a theory) was one of the things that indicated that it did not. Not to mention, the theory that is now called “big bang” is traceable back to Lemaître, who did not specify a “bang” in particular anyhow.
Arp, being an atheist, would of course attempt to devise a cosmology that did not involve a Creator. And there is still a lot of confusion as to whether CERN actually did find a Higgs boson that complies with the standard model or not.