We don't know anything at all about the physics of infinitely small spacetimes, because we don't have a fundamental physics of spacetime at all.
GR is a descriptive approximation of the behaviour of spacetime, but says nothing about the fundamentals that generate that behaviour.
> If time effectively halts at T0, then what possible event could occur (outside of time?) to nudge that infinitely large glob off mass into the motion we observe today?
Anthropic principle explains it. If you need a Prime Mover, you can also replace it with Anthropic principle and random chance.
For example if time halts at T0, physics breaks. Using limes when t->0 you get that v-> Infinity (or c). Slower time moves for you, faster you move in space. At that point, if nothing is there to detect it, every massless particle will be effectively everywhere, all at once. Essentially photons can have Infinite energy and just cause a random Big Bang. This is CCC like explanation.
Another answer is Hawking's North of North Pole time problem (from Universe in a Nutshell). If time halts a T0, you can't ask what's before it. It's just logical impossibility. Like what is North of North Pole? Answer is: Question is invalid. Anthropic principle implies there are however many multiple such configuration so you get a parallel or sequential universe solution.
We arise and wonder how exactly Universe exists that support life, even if we can clearly see, it's only supporting life at this moment. Our existence is a grain in the sand of a universe-sized sand clock that will be the Black Hole epoch.
The universe advanced from T0 because it had to, by definition.
If this seems like a weird cop-out, well, that’s a singularity for you.
Yes.
If you assume that all events have causes.
Our understanding of the world (aka science) is largely based on causality, and if things existed without any cause or reason, our understanding of "science" would probably be very different.
(I'm not a physicist, but this is how I understand things.)
Also, no one is "lazily tossing it aside". It comes out of the mathematics that describe the observations:
Say you find that all observations you make are perfectly described by dx/dt = 1/x with current time t1. If you follow the trajectories backwards, you find that the trajectory can not be extended back past some initial time t0 at which x(t0) = 0 as the equation becomes singular then. You are now at time t1-t0 from the initial singularity. That is the age of the universe since the big bang. Now the trajectory as it approaches t0 has some unusual properties, it moves infinitely fast, etc... These might lead you to postulate that unknown physics will actually invalidate your law as you approach t0. But there is nothing logically or epistemically _wrong_ with the law you have. The finiteness of time flows out of a causal empirical induction argument. It is not introduced ad hoc to avoid some difficulty, it just is how we find nature to be at the most conservative interpretation of the evidence.
You stop at the uncaused first cause or the unmoved mover, of course.
Think of it like a particle decaying - at some point it just happens with no trigger or internal mechanism, and now you suddenly have the decay products wizzing about with some energy and momentum that they just start with.
There is no reason to assume that everything has a cause. It is perfectly logically consistent to have things without cause in the universe.
There are proposals for time stretching infinitely back, but we have almost no way of testing them.
The big bang could not create universe from nothing, it could only spread matter from a singularity into ever expanding universe (time-space).
is it even possible, to have entirety of universe matter and energy in a single point?