I think it would be better if we restricted our discussion with respect to Classical General Relativity. A Quantum Version has not yet been completetly framed, so why predetermine what a Theory of Quantum Gravity has to say. It has been shown that there was a singular solution to the beginning of the Universe and the singularity solution is consistent with the existing theories on the Beginning of the Universe. So I don't see any problem in the singularity solution given by Classical GR. You don't have to see singularity as a place with R = 0. R cannot be a perfect zero since space is quantized, however, you could assume a singulrity to be a really small region of space-time, probably of the order of planck length and time. So I don't think we need to wait for a theory of Quantum Gravity in order to predict/reject singularities. Singularities should exist, where else would you think can there be a better link between GR and Quantum Gravity. It is at these singularities that QM and GR meet . So why avoid them?