Is space-time discrete or continuous? Opinion among experts seems to be divided or uncertain. It could be either, both (or neither!).
Prior to the capacity to experience time and space is the capacity to experience distinction and continuum, simultaneously.
Even if reality turns out to be discrete, each discrete part will form a continuum of its own. Reality will always be both.
The dispute about whether the universe is really discrete or continuous reflects the limits of our capacity for conceptualisation. It is really a dispute about the nature of our own minds.
When describing the universe at its deepest levels we tend to use the same kinds of approach that we use when looking at nature at our the human level; we tend to pitch ourselves as external observers, looking at the universe as though it were a rock on a table or lizard in a jar, and make observations or measurements about it from the outside looking in. But this is not a position we can take with respect to the cosmos. Not only are we inside it, we are synonymous with it on the grounds that it is formed in our own mental image.