Does your/theirs/anybody's theory establish that anybody's future exists?
At the risk of repeating myself...
In terms of the science we have General Relativity as
the theory of space and time
*. The structure of the theory is such that it is impossible to divide the whole space-time manifold up into past, present and future.
Even if we pick one event (point in space-time), although we can identify other events that are unambiguously in its future and others that are unambiguously in its past, we are left with a whole region of events that are
space-like separated from it and might be in its future or past depending on what reference frame we look at things from.
Since we can't even identify "
The Future", it is difficult to se how we could give it a different status from the past or present.
And if it does exist how can it be examined empirically?
It's not that we can empirically examine the future, it's that our empirical investigation of the nature of space and time has led us to construct a model that rules out assigning a different status to "
The Future" simply because "
The Future" isn't actually a thing.
* Leaving aside some eccentric conjectures, even hypotheses aimed at unifying GR with QFT (string theory, loop quantum gravity etc.) approximate to GR at 'low' energies.