  A fundamental problem of out-of-equilibrium physics is the speed at which the
order parameter grows upon crossing a phase transition. Here, we investigate
the dynamics of ordering in a Fermi gas undergoing a density-wave phase
transition induced by quenching of long-range, cavity-mediated interactions. We
observe in real-time the exponential rise of the order parameter and track its
growth over several orders of magnitude. Remarkably, the growth rate is
insensitive to the contact interaction strength from the ideal gas up to the
unitary limit and can exceed the Fermi energy by an order of magnitude, in
quantitative agreement with a linearized instability analysis. We then
generalize our results to linear interaction ramps, where deviations from the
adiabatic behaviour are captured by a simple dynamical ansatz. Our study offers
a paradigmatic example of the interplay between non-locality and
non-equilibrium dynamics, where universal scaling behaviour emerges despite
strong interactions at the microscopic level.
