We report on the fast production and weakly destructive detection of a Fermi gas with tunable interactions in a high finesse cavity. The cavity is used both with far off-resonant light to create a deep optical dipole trap, and with near-resonant light to reach the strong light-matter coupling regime. The cavity-based dipole trap allows for an efficient capture of laser-cooled atoms, and the use of a lattice-cancellation scheme makes it possible to perform efficient intra-cavity evaporative cooling. After transfer in a crossed optical dipole trap, we produce deeply degenerate unitary Fermi gases with up to 7 x 10(5) atoms inside the cavity, with an overall 2.85 s long sequence. The cavity is then probed with near-resonant light to perform five hundred-times repeated, dispersive measurements of the population of individual clouds, allowing for weakly destructive observations of slow atom-number variations over a single sample. This platform will make possible the real-time observation of transport and dynamics as well as the study of driven-dissipative, strongly correlated quantum matter.