How can we know if our big bang is a one side of a wormhole? According to Hawking, he proved that (excluding quantum mechanics) the big bang started at a singularity. Hence showing a connection between the mathematics of the big bang and black holes.
Equally, looking out at the Observable Universe we are looking back in time, and in any direction we eventually will see back to the big bang singularity. Or at least to the event horizon of that singularity.
Hence, the observable Universe (or any time-slice of the Universe that has bounds at the big bang) could be represented on the surface of a sphere with you at one pole and the big bang singularity/event horizon at the antipode. Like a giant black hole on the far side of the sphere.
Now, according to solutions of General Relativity a blackhole can be a wormhole. According to Susskind and others, this is the equivalence of two entangled black holes.
For our big-bang / observable-universe-horizon, if this was a wormhole it would, presumably, have to link to the big bang of another mirror universe running in the oppose direction. (I suppose this is just like the trick in electrostatics where it is useful to assume a mirrored version of a half-plane in order to get good boundary conditions).
In fact if this were true, (a 2D slice of) the observable Universe might resemble the top surface of a pizza, with the bottom of the pizza as the mirror universe, and the rim of the pizza as the big-bang event horizon. Every black hole could be a wormhole tunnelling through the pizza to the other side.
So, anyway, I wonder if there would be any tests or consequences we could measure to tell if our big bang was one side of a wormhole. (I am not sure if this is related to the tunnelling hypothesis of Quantum Cosmology). Or whether the wormhole hypothesis could be merely a mathematical trick with no Platonic reality to it. If it was a wormhole, would this be considered a boundary condition for our Universe? i.e. an initial condition?
 A: Drawing on work by Gasperini, Smolin, Guth, and many others, the Polish-American physicist Nikodem Poplawski has formulated a cosmological model, described at https://www.sciencedirect.com/science/article/pii/S0370269310011561#br0420 , which does appear to have the potential verifiability that you are seeking.
In Poplawski's model, any large rotating star (-most stars are generally considered to have at least a faint residual rotation) would collapse gravitationally, upon an expenditure of its nuclear fuel sufficient to leave it without radiation pressure adequate to resist such a collapse.  Fermions formed by the separation of the particles from antiparticles, in pairs previously only virtual, would be spun outward by their contact with the vastly larger fermions of the star itself, thereby forming a new "local universe", causally separated from the multiverse (potentially eternal both to the past and to the future) of its origin, where it would appear to be a black hole. (At least 90 black holes have been identified, generally by the elliptical orbit still followed by their former partner in binary pairs:  About half of all stars are usually considered to be binary.)
As described in a paper by Daniel Linford at https://arxiv.org/abs/2006.07748 , the "arrow of time" in each local universe of Poplawski's multiverse would inherit the directionality of passage through time from its "parent", the LU within which the BH would've appeared:  Consequently, there would be a slight prevalence of a particular direction of motion within every LU.  Such a prevalence has been spotted by the astronomer Lior Shamir, although it might be faint enough for the visibility of that prevalence to vary, at least on the usual assumption that stars are still being formed.
Although Linford's paper was written in the aftermath of the philosophical debate between the physicist Sean Carroll and some theologians, his analysis does appear to leave some slight potential for creationism through artifice, as the addition of relatively small amounts of mass to large rotating stars, by phenomenally advanced civilizations, might, with extreme rarity, allow for the formation of new black holes within any one of Poplawski's local universes, whose individual shapes Poplawski has analogized to the skin of a basketball.  (The mindless violence unleashed over Ukraine makes it seem extremely unlikely that our own civilization might ever last long enough to play such a role.)
