"Solid" doesn't really have meaning at the sub-molecular level. All space has something in it, even if it's just vacuum energy. Virtual particle pairs come and go all the time. Some space has particles with electromagnetic charge. Each of these has some interaction radius. Technically, this is infinite. Electric field reaches everywhere, but thanks to inverse square law, only other particles within some much smaller radius than infinity will interact with enough force to change velocity noticeably. Gather together a large enough collection of these into chemically bonded distinct macroscopic objects, and there you go. The radius at which particles are repelled from each other is smaller than the distance between these bonds. That's all "solid" means.
Whether particles truly have any material extent at all, or are simply literal points representing the center of various interaction radii, is unknown and probably unknowable. It's not even clear what the difference would mean. Can a particle somehow "take up space" and prevent another particle from occupying that space if it interacted with no force at all? I'm not a physicist and kind of talking out of my ass here, but I think the Pauli exclusion principle implies maybe, but it doesn't apply to all particles.
Human perception relies entirely upon electromagnetism. Once you get down to distances less than the wavelength of the highest frequency photons and electrons, we can probe and describe the relationships mathematically, but I don't think it makes sense to try and conceive of what these things "are" in some greater ontological sense. We inherently analogize to what things look and feel like, but looking and feeling like anything is a higher-level emergent phenomenon of electromagnetic interactions.