How about during the 1970's at SLAC where they hit proton rich targets with relativistic electrons and were surprised by evidence of deep inelastic scattering (think Rutherford and the atomic nucleus for an analogy). Analysis of the experiments indicated that electrons were smashing into something very, very tiny and very, very hard inside protons. These experimental results combined with theoretical work being done at the time opened a whole new understanding of particle physics. Quark theory helped explain the physical results of experiment. (See Michael Riordan's "The Hunting of the Quark: A True Story of Modern Physice .)
Of course, no one can "see" quarks; confidence in the analysis and interpretation of the experimental results must come from many experiments, detailed analysis and much theoretical work, which, by the way, has happened since the turn of last century. Please see Harvard's Peter L. Galison's works "How Experiments End" (1987) and "Image and Logic" (1997) for how physics can claim a high degree of certainty in experimental results. (Note: There may be more recent works on this topic.)
Although not exactly on topic, I must quote someones insightful sig: "In science nobody believes the theory except the theorist and everybody believes the experiment except the experimentalist."