To my understanding, white holes are hypothetical objects that are time-reversed black holes; black holes gravitationally "suck in" matter whereas white holes "spit" matter back out. As such, I think it's a nice idea that the Big Bang could be the "spitting of matter" via a white hole (assuming such an object exists).
This got me wondering how one could experimentally test for such an object. Since the expansion rate of the universe is increasing, could one possible explanation be that a white hole is continually "spitting out" matter such that an increase of flux of in-falling matter/space could be observed as an increasing rate of expansion of out-pouring matter/space? While I don't know of a way to detect this, I was wondering whether the following idea was fruitful or not.
Given that a supermassive black hole is believed to be at the center of every galaxy, given that most galaxies (sans Andromeda) are receding away at a speed proportional to their distance relative to us observers, and given that the spatial distribution of matter in our universe is isotropic and homogeneous, could one build a simulation of such a concept? To emulate isotropy and homogeneity, one could use a random number generator corresponding to a uniform distribution to place "galaxies" along a grid; accounting for gravitational forces, one can simulate the time-evolution of these galaxies and compare rates of in-falling matter to find a correlation between the rate of in-falling matter and the expansion rate of the universe (likely as a function of time-elapsed, and age and size per black hole). While the simulation does not definitely prove anything, providing a correlation could be interesting in my opinion.
Is this a stupid idea, or is there a potential to build upon this idea? If it is not fruitful, I am curious as to why.