  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 $7
\cdot 10^5$ 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.
