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"We are observing phenomena that give rise to the theory that there was such thing as a "Big Bang.""

Just as we're observing the phenomena that gives rise to the theory that evolution happens. Specifically, we see genetic variation, we see genetic mutations, and we see natural selection. None of those driving forces are in question - the only question with evolution is, if you let those forces interact over extremely long periods of time in various, changing conditions, will things happen the way the theory of Evolution says they'll happen? Thus far, our best evidence is to look at the horribly incomplete fossil record to try to map out as many different species as possible. With more of the fossil record available, and with modifications to the theory of Evolution made to deal with anything unexpected that's found, we should be able to accurately map out much of the rest of the fossil record and then set about the job of verifying that. That's probably about the best test we're going to have with evolution.

"It is certainly a plausible theory, but like theories of evolution, no more "provable" than the existence of God, and thus no more worthy of consideration in the marketplace of ideas."

The difference between the Big Bang theory, the theory of Evolution, and the existence of God is that the first two are physical and conform to natural laws, where as God is metaphysical, and thus is beyond the testing or consideration of good science. As for the provability of the Big Bang or Evolution, it's certainly true that neither can be proven beyond a shadow of a reasonable doubt (not to mention, plenty of unreasonable ones). That being said, both have foundations upon which they stand, and both are able to be used to make certain predictions. With the Big Bang, we should be able to detect certain kinds of radiation in certain places, and certain types of matter decay should occur. We can test for those things. If things don't add up to the predictions set forth in the theory, then the theory must either be adapted to compensate (if possible) or be scrapped completely. The same goes for the theory of Evolution. Thus far, while questions do most certainly remain, nothing has struck a fatal blow to evolution theory.

There are certainly situations which would do so, such as evidence of organisms which have remained the same species for periods of time far beyond anything with which the ToE can cope. A statistical model could indeed be put together at some point which shows that the likelyhood of successful mutations for certain species at certain times, even when combined with genetic variation, cannot begin to explain events in the species' history. An example would be an extreme change - a lizard sprouts wings and flies in an incredibly short period of time. With enough dormant genetic material, an intelligent designer could indeed make just such a thing happen. The ToE would be at a loss to explain it, and all but the most zealous supporters of the ToE (who are absurd, in my opinion) will have to look elsewhere for an explaination. While the Big Bang and the ToE may never be conclusively 'provable', both are indeed quite disprovable. Theorists can dance around problems in quite a few ways, but getting their peers to accept fancy footwork is quite another challenge.