> Well, there's also the possibility that the universe occupied some single state (say, the singularity posited by the big bang theory) since t=-inf to some t0 when it exploded
What's the actual difference between these two positions:
(A) the universe was in state X for an infinite amount of time, then suddenly transitioned to some other state Y
(B) time began at t=0 with the universe in state X, and it immediately transitioned to some other state Y
They seem effectively identical, with seemingly no way for us to tell them apart. (B) seems simpler than (A), so by Occam's razor we ought to prefer it to (A), unless we have some specific reason not to. What could such a reason be? Well, I suppose (A) might lead to simpler mathematics. However, in actual fact, I don't believe that's true; and even if it were, it still might be reasonable to conclude that the "infinite static before-life of the universe" was just a mathematical artefact, without any physical reality.
Other problems with this view: (i) time is usually understood as a succession of instants which are somehow distinct – could an infinite succession of instants, all exactly the same as each other, actually count as "time"? (ii) why, if the universe had existed forever in a single state, did it suddenly transition to a new one? That seems harder to explain than the universe just existing with a finite past.
So, I think an infinite past only really makes sense if the infinite past involved an infinity of distinct universe-states – which I think might lead to the consequences I was suggesting.
> In this model, the universe has an infinite number of possible states, and is in fact guaranteed to never visit a previous state, even though it has an infinite future ahead of it.
Let me present a variation on the Boltzmann brain argument: the universe is vast, yet the volume of it which is actually relevant to humans is quite small. Humans cannot ever know or care about the state of the universe as a whole, only that subsection of it we can somehow observe–which is at most the observable universe; but, if we accept the possibility (even only as exceedingly unlikely) that nature is deceiving us (other galaxies don't really exist, it is just randomly arranged photons which by amazing fluke are exactly the same as what we'd observe if other galaxies did), the knowable subsection could be a lot smaller. No matter how stupendously unlikely such as scenario may be – so long as its probability is not strictly zero, in an infinite future, any constant non-zero probability is going to converge to unity.
Consider the current state of this galaxy – does Lambda-CDM guarantee that the universe will never visit a future state, which contains a Milky Way-sized volume, whose state is exactly the same as the state of this galaxy right now? You can repeat the question for "solar system-sized volume with exact same state as our solar system has right now" or "Earth-sized volume with exact same state as Earth has right now". Or a volume with the same size as the current observable universe, and the same state as it?