that possibility is being investigated.
There may be reasons why it is impossible.
But if you pose the question very generally then I personally have not heard anything that rules it out.
There are many papers that study the possibility that the bigbang could have been preceded by some kind of gravitational collapse. that idea is pretty well developed, although not checked. The question is, what kind of collapse?
would it necessarily have been the collapse of a whole universe---a "Big Crunch?" Most of the research explores this possibility. this kind of picture is called a "Bounce".
or could it have been a more modest gravitational collapse----the formation of a black hole in a prior region?
this is harder to imagine and has not been successfully modeled yet (unless in grossly oversimplified form.)
I will get a link to some recent technical articles. At the moment they have only crude simplified models and the work is preliminary. I don't think you can draw any clear yes or no conclusions, but I will get a sample of current research and you can decide for yourself.
here is one by Bojowald
http://npg.nature.com/nphys/journal/v3/n8/full/nphys654.html
here commentary by Rovelli
http://npg.nature.com/nphys/journal/v3/n8/full/nphys690.html
I sense that these are landmark papers in a sense, even though quite short and relatively untechnical (not just for specialists-only). their publication in the journal NP signals a change in the intellectual climate.
here is a brief exerpt from what Rovelli had to say
Science has frontiers; sometimes these frontiers move. One of the most impressive of science's frontiers is the Big Bang, and now a quantum theory of gravity — loop quantum gravity — is providing equations with which to explore it. Although these equations are still tentative, and rely on drastic approximations, they introduce a definite method of exploration, and are capable of describing the Universe not only close to the Big Bang but also beyond it. It is in this context that Martin Bojowald reports, in this issue, on the possibility of a peculiar limitation to our ability to observe fully the 'other side' of the Big Bang — whatever that expression might mean (Nature Phys. 3, 523–525; 2007).
Here is some earlier discussion in a PF thread about the above
https://www.physicsforums.com/showthread.php?t=175704
Here is a recent paper by Kevin Vandersloot about resolving the black hole singularity (what comes "after" or "out the bottom of" a black hole)
http://arxiv.org/abs/0709.2129
Loop Quantum Dynamics of the Schwarzschild Interior
Christian G. Boehmer, Kevin Vandersloot
15 pages, 13 figures
(Submitted on 13 Sep 2007)
"We examine the Schwarzschild interior of a black hole, incorporating quantum gravitational modifications due to loop quantum gravity. We consider an improved loop quantization using techniques that have proven successful in loop quantum cosmology. The central Schwarzschild singularity is resolved and the implications for the fate of an in-falling test particle in the interior region is discussed. The singularity is replaced by a Nariai type Universe. We discuss the resulting conformal diagram, providing a clear geometrical interpretation of the quantum effects."