I noticed there are a bunch of 'big bang' posts. So, why not throw my hat into the ring.
There are a few major reasons the big bang cosmology is accepted.
1. the redshift of clusters of galaxies in a very specific relationship, the ones farther away do so at a faster rate than the ones closer by. Look up the plots. They are beautiful.
2. the relative abundances of elements. Yes, the big bang model specifically predicts that the universe ought to be about 75% hydrogen, 25% helium (with fudge for 'rest', including a bit of lithium). These predictions get a lot more specific about this by the way, predicting also what percentages of isotopes we ought to see.
3. cosmic background radiation, the common afterglow of the fact that the observable universe used to be in very close quarters. The very small perturbations of this are also important.
In addition, there is recent evidence for the inflationary model by being able to detect specific kinds of gravitational waves from BICEP. Future looks at gravitational waves could provide additional looks at the very early universe.
Why I am posting this-- specifically because this section is taken over by believers with a very narrow viewpoint on what is an acceptable reading of Genesis and limited understanding of the relevant science. While I am hardly an ideal believer, I am still around for one reason or another, and I still think it is important that believers and non believers alike see this diversity in the body of Christ. You do not have to be scientifically illiterate or alternatively reject the scientific consensus to be a member. I don't think this has any direct relevance to God's existence or creative action and find the emphasis put on that distracting and unfortunate, and for some of us, straight up deflating.