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.