It's inductive and abductive reasoning. The one field, and it has lot of mathematical characteristics which makes it unique on its own, and also it is the only one that has a chance to fit, is the e8 field popularized by Garrett Lisi.
If a universe were to be designed based using the e8 Lie algebra as an elemental field, it would look a lot like our universe.
Currently the standard model is a patchwork of field added as experiments for observing particles were possible to realize. The big picture's view is a unified theory which fits perfectly all existing data.
Currently, we don't have any theory that works that's any simpler than the SM. So that's the theory that Occam's razor currently tells us must be true, as it's the simplest alternative that actually works.
It seems there has to be a reason WHY there are exactly N fields, and WHY they interact in the ways they do.
Edit: As I noted in another comment, the best explanation may come down to "there are only 100 viable types of universe, and ours is type 42". I'd be happy with that.