As I see it, there is some fundamental basis the SM is built on, and that's the spacetime structure of special relativity (Minkowski space) implying that the quantum theory should be constructed from the unitary (ray) representations of the proper orthochronous Poincare group. Then in practice it has turned out that the (so far) only successful formulation comes from local quantum field theory formulations, i.e., leading to the usual notion of massive and massless fields transforming locally under the Poincare group and then being reduced to the unitary irreducible pieces, each defining a fundamental field/particle. This particularly implies that massless fields/particles with spin ##s \geq 1## are necessarily gauge fields.
The "rest" of the standard model, which is considering the question, what's "the matter content of the universe" then is based on finding the gauge groups and their representations leading to consistent local QFTs describing the observations, and that has been found by an interesting interplay between theory and experiment, and it's very likely not to be finished since the SM most probably does not provide the complete set of fields/particles needed to describe all observations (in terms of the cosmological standard model what is the "dark matter" made of needed to get the amount of "clumping" to form the observed inhomogeneities like the galaxies, galaxy clusters, and so on, as well as an understanding of why the cosmological constant/dark energy density takes the small value it does).