I think the meaning of “imperceptible” is critical to the question. Even quarks, to use your example, aren't imperceptible as i understand it. Experimental devices respond more or less consistently as they're expected to if physical models with quarks accurately reflect reality—quarks are real, and their effects are perceptible.
Yes, of course i accept non-constructive existence proofs. A proof is still very much a physical, (socially) tangible act.