It is, by Hume's Fork, impossible to prove.
There are certain propositions made in Buddhism which are empirically verifiable. One can generally not dispute the conditioned nature of practically every observable datum. The consequences for this conditioned nature leads to the 3 Signs. Specifically, in AN 3.47a, we see another description of the "sankhatassa sankhatalakkhana" as including the observable fact that a conditioned thing is subject to arising, falling away and change. AN 3.47b then discusses the opposite, ie the 3 asankhatassa asankhatalakkhana, namely non-arising, non-falling away, and no change. One could then logically infer a priori that Nibbana is irreversible.
But, can one, on the basis of the observation of conditioned states, surmise that there is an "unconditioned"? The "unconditioned" does not seem to be empirically observable, so that leaves only 2 choices for a proposition concerning the "unconditioned" to be meaningful.
One could take this as a matter of faith, in which case it becomes soteriologically meaningful within that religious discourse.
The alternative is of course to rationalise it via metaphysics. Unfortunately, I don't believe Kant made a convincing case for any meaningful discourse on synthetic a priori propositions. A statement about the "unconditioned" is synthetic to the extent that its truth value is independent of and additional to the statement concerning the "conditioned", and yet it presumes to be derived logically from the statement concerning the "conditioned" - thus the a priori appellation.
It's a lost cause, since Hume pointed out the futility of this enterprise more than 2 centuries ago.
And I'm happy to take the irreversibility of Nibbana on faith alone.