A similar question: does time evolve in discrete steps, or is it continuous?
The passage of time can only be established by comparing with physical phenomena that evolve over time. Even if that comparison would suggest "discrete steps", that doesn't exclude the possibility of time evolving continuously, but instrument / experiment too 'crude' to see between steps.
Right up there with "are we living in a simulation?", and "does $DEITY exist?". As long as you can't break into a deeper layer (assuming that exists!), it's undecidable, and a philosophical rather than a scientific question, imho.
but what would be the alternative?
On the other hand it may indeed be a remarkable feature of the human mind that it can "make mathematical sense" of subsets of reality, but there is no overarching system and no reason to expect that we will be able to make simultaneous mathematical sense of "everything".
It might take a long time to collect sufficient such "metadata" to help tilt the balance.
The interesting bit (pun) is that this seems to be a recurring pattern. Whenever there is a intellectual revolution that establishes new ways of thinking / acting, there is a tendency to apply its toolkit to everything in sight, including "the big questions".
So it was with the industrial revolution and the hordes of related engineers: the universe was invariably seen as "a machine". With the digital revolution and the hordes of computer engineers, the universe is invariably "a computer". Effectively just a glorified version of the law of the instrument [1] "to a person with a hammer everything looks like a nail".
The controversial question (and one that cannot be dismissed easily) is whether the universe is in some broader sense "mathematical". The huge success of mathematical descriptions around certain corners of the universe makes people think there might be something to it. But maybe mathematics too, is just our hammer.
[1] https://en.wikipedia.org/wiki/Law_of_the_instrument