AspE, since the entity God is, by definition, supernatural (that is, existing beyond nature), He/She/It/They (simply "He" for future reference) would not be constrained by the limitations of the physical universe. Therefore, it would indeed be possible for Him to survive the Big Bang, and even to foresee the possibilities inherent in the universe He created. (After all, if He existed within the universe, He could hardly have created it - He would have had to exist first, in order to do the creating.)
Sling, I don't know what cosmologists you've been talking to, but the monobloc, the singularity from which the Big Bang banged, was not subject to any laws of physics - the initial conditions were too chaotic for any laws of physics to apply until a fraction of a second after the Bang itself. It did not "come from nothing" - it came from, for lack of a better term, its own possibility (or possibly a supernatural Being saying, "Let there be light!"). No cosmologist claims to know how the Bang happened; the topic stands outside science, as it cannot be understood using the laws of the universe that came from it.
This is not the same as saying, "God did it!"; argument from ignorance is a logical fallacy. Rather, this is saying that you can hold whatever beliefs you like, and no one can disprove them (or prove them - the converse holds as well, after all).
Your statements regarding evolutionary theory are unrelated - cosmology has nothing to do with biology - as well as being inaccurate (the Cambrian explosion, for instance, would be the expected outcome of the pre-Cambrian extinction, apparently caused by a sudden planetary climactic shift - most probably due to asteroidal or cometary impact), and will thus be summarioy ignored, just as I would ignore someone claiming to prove that pi was equal to exactly 3.5.
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Sodium is a metal that reacts explosively when exposed to water. Chlorine is a gas that'll kill you dead in moments. Together they make my fries taste good.