No, we cannot see individual quarks within protons and neutrons directly. Quarks are elementary particles and fundamental constituents of matter, but they are confined within particles such as protons and neutrons due to a phenomenon called color confinement. Color confinement is a fundamental property of the strong nuclear force, which is responsible for binding quarks together.
The strong nuclear force is mediated by particles called gluons, which interact with quarks. However, unlike the electromagnetic force, which becomes weaker at longer distances, the strong force becomes stronger as quarks move apart. This means that the force between quarks increases rapidly with distance, making it virtually impossible to separate a quark from a particle and observe it in isolation.
The strong force is so strong that when you try to separate two quarks, the energy stored in the field between them increases. At a certain point, the energy is sufficient to create a quark-antiquark pair out of the vacuum, effectively preventing the isolation of individual quarks. This phenomenon is known as quark confinement.
As a result, we can only observe composite particles like protons and neutrons, which are made up of quarks, but not the individual quarks themselves. We infer the existence and properties of quarks through experiments, theoretical models such as quantum chromodynamics (QCD), and indirect evidence from high-energy particle collisions.