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Can you see or accurately visualise sub atomic particles or are they known only by maths and/or inference?

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You can see a nucleus and the nucleus of a hydrogen atom is a proton which is the same. You can't see below that at least with a source of neutrons that ISIS produce, but you can see down to the level of the proton.

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We can image the sub-structure of nucleons by a number of different techniques involving high energy scattering. The results are generally presented in terms of "parton distribution functions" or "structure functions".

One such experiment that I had some small relationship with (though not enough to be an author) was NuSea (E866) at Fermilab in the mid 1990s, which used muon Drell-Yan as the a probe to image the QCD sea in particular.