A personal observation FWIW. Maybe somebody else will find it helpful.
I try to avoid using the term "Big Bang" both in writing and in my own thoughts. It is used so vaguely in so many different ways that it really has no meaning.
Instead (see if this seems reasonable) I talk about "the start of expansion". We see distances expanding according to GR--if we follow it back it seems it must have begun somehow. So "the start of expansion" has some simple concrete meaning--at least to me.
Different theories or models represent the start differently, so they would give different answers about conditions (density, size of what became the currently observable region, matter content if any, evolution of the Hubble expansion rate i.e. inflation or no-inflation, etc etc).
IOW there is no one "Big Bang". There are different versions of the start of expansion. So asking questions about the "Big Bang" (as if it meant something definite) tends to lead to confusion.
For me the easiest version of the start of expansion to imagine, and read research papers about, is the LQC
bounce. There you have estimates of the density at bounce. You have computer models run under a variety of conditions---and a solvable equation model. You have definite predictions that can be tested by further observations of the CMB. For example see the recent paper by Ivan Agullo
Just google "agullo lqc predictions" and you should get
http://arxiv.org/abs/1509.05693
Detailed analysis of the predictions of loop quantum cosmology for the primordial power spectra
We provide an exhaustive numerical exploration of the predictions of loop quantum cosmology (LQC) with a post-bounce phase of inflation for the primordial power spectrum of scalar and tensor perturbations. We extend previous analysis by characterizing the phenomenologically relevant parameter space and by constraining it using observations. Furthermore, we characterize the shape of LQC-corrections to observable quantities across this parameter space. Our analysis provides a framework to contrast more accurately the theory with forthcoming polarization data, and it also paves the road for the computation of other observables beyond the power spectra, such as non-Gaussianity.
24 pages, 5 figures
Or if you don't recall Agullo's name, just google "lqc detailed predictions".
That also brings up the paper as the first hit.