In our basest theory QFT, no particle is fundamental because they're actually "fields" - but those fields are fundamental so that doesn't answer your question. We just think they're fundamental because we don't have enough evidence to construct anything better than the Standard Model.
It's not possible to do better than that, though, because you can't prove a negative statement like "there are no more fundamental particles". Even if we understood the laws of physics completely, they could always change on us. It's all up to the guy who owns the universe simulator.
But doesn't fundamentality in fields imply something quite different than fundamentality in parts (particles)?
I sense that the next step in physics and ontology can only happen when we have created a new linguistic approach to capture the 'fundamental' idea here.
If information is physically fundamental, the fundamental "particle" would be some sort of bit. Planck's constant could be that bit.
All other particles would be derivative, and their being caused by some base rules.
Physics will only be complete when fully explained in terms of information, regardless of the physical reality of information. The two aspects of explanation are 1. the rules and 2. what are the bits? Perhaps both those things are one.
Perhaps bits are not fundamental and quaternary bits are, but that would still implicate information as fundamental.
