Then I would assume that the problems I've cited would apply to the extremely hot state, having no place to exist, no outside of and no time in which it could have existed.
Is this state called the singularity? If not what would you call it?
It would seem you have a misconception regarding the Big Bang model.
At T=0, you cannot say there was "no time in which it (the Universe) could have existed." T=0 is simply a coordinate, a location in time, which is a dimension in the same sense as the spacial dimension. To say that "time did not exist at T=0" is not true; you could say that the concept of "before" T=0 does not make sense in the same way that asking what is North of teh North Pole does not make sense, but in no way is there a suggestion that there is "no time in which it could have existed."
Similarly, at T=0 the
spacial dimensions length, width and height were "smaller" than they are today. In fact, it is the constriction of the spacial dimensions (a reversal of the directly observed expansion of the Universe) that
causes the extreme density and heat of the first moments - all of the energy and matter in the Universe were compressed into a very small volume.
But again, saying that the spacial dimensions were smaller than they are today, even to the degree where the entirety of the Universe was compressed to a size analogous to a modern
atom, still does not suggest there is "no place" in which the matter and energy of the Universe could exist. It's true that it did
not exist in the form we see today, as it
was too hot and too small for conventional atoms and subatomic particles - it took time for the Universe to expand and cool down enough to form even protons and electrons from the quark-gluon plasma. But again, the Big Bang model does
not imply there was ever "no space," just as it does not imply that there was ever "no time."
The "no outside" bit is a conundrum. There may be additional dimensions of which the four dimensions of space and time that comprise our Universe are but a subset, meaning there could be multiple Universe existing in a fifth dimension of sorts. But the Big Bang model doesn't involve such things - there are hypotheses out there that suggest additional dimensions, but they aren't relevant to this discussion as they have been inadequately tested (as far as I understand, they are mathematical models that require testing to determine accuracy and relevance to reality).
The singularity is the point at which the mathematics and laws of physics we currently use stop making any sense when applied to the state of the Universe. In the time between T=0 and T=10^-43, which is the barest, tiniest fraction of a second, we cannot describe the Universe or make meaningful testable predictions regarding the Universe because of the extreme conditions of density and heat. We require additional information regarding high-energy physics to venture into that bare moment, and scientists are working on experiments to gain that information as we speak.
So your "problems" with the Big Bang model don't really exist. There is no point in the existence of the Universe where there is "no time." There is no point in the existence of the Universe where there is "no space." Time and space are features
of the Universe, and your "problems" are analogous to saying "your model of water doesn't work because there was no wet." "Wetness" is a property of water; when discussing the Universe, time and space are basically what we're discussing, and can never be said to "not exist" without the
Universe not existing.
And of course the Big Bang is
not a model of the "origin" of the Universe in terms of explaining why it exists; it is a model of the observed
expansion of the Universe, with testable predictions regarding the past all the way back to T=0.
™ Version 4.2
