that is something which interested young people like yourself will have to determine----perhaps other PF posters have ideas
I can only comment at level of inconclusive detail
LQC does not "postulate" a bounce
it is the result of calculating a wave function evolving across the classical singularity
the math is pretty simple: all standard cosmology is based on two short diff eqns called Friedmann eqn, if you (loop) quantize them you get again a comparatively simple difference equation model and it does a bounce (changing from contraction to expansion) right at the point where the classical Einstein/Friedmann model blew up
The people who worked it out---Martin Bojowald, Abhay Ashtekar, et al---call it a bounce (I did not hear them say "Big Bounce" actually, but they do say bounce). It is not my choice of term.
There is an incredible difference between LQG and other approaches which it will help to understand. LQG is extremely conservative----bare bones quantization of GR with no additional structure beyond what is required by quantization----no "creative" elements---no "branes" and no "extra dimensions" and "ToE"stuff.
It is the bare minimum and people have been trying to quantize GR for several generations (since before 1950) and there'v been technical obstacles and they'v finally gotten over some of the obstacles and it's beginning to work.
There is a small set of versions of LQG and they are all beginning to predict numbers that will allow them to be tested and some will be rejected and modified----the cycle of prediction and experimental test will help the development.
The bounce in cosmology is a robust result in the sense that it is predicted by any version----LQC is a simplification of LQG so whatever version of the full theory boils down to very similar versions of cosmology all with the same qualitative behavior.
It is very hard to compare this rather concrete, limited nuts-and-bolts result of doing a standard ("canonical" they call it) quantization job on 1915 GR with "M-theory" which seems a total opposite-----highly un-conservative, non-predictive, proliferated into a huge variety of versions none of which corresponds to reality in any obvious way. Different animal(s) I'd say.
How are you on the key concept of background independence?
The 1915 General Relativity theory is fully background independent----invariant under diffeomorphisms (smooth transformations of the manifold). It is an awfully important feature of GR that many people fail to recognize.
LQG preserves the background independence feature---it is also a background independent theory, like GR itself.
This is why it is so hard to compare LQG to stringy theories. Or to draw any solid connections. The connections tend to be spurious, specious ones "this contains
that" when it doesnt really contain it except in some superficial way.
to understand the basic theoretical layout you need to assimilate the background issue. unfortunately. seems to be a major hurdle for a lot of people