  Periodically driven quantum matter can realize exotic dynamical phases. In
order to understand how ubiquitous and robust these phases are, it is pertinent
to investigate the heating dynamics of generic interacting quantum systems.
Here we study the thermalization in a periodically-driven generalized
Sachdev-Ye-Kitaev (SYK)-model, which realizes a crossover from a heavy Fermi
liquid (FL) to a non-Fermi liquid (NFL) at a tunable energy scale. Developing
an exact field theoretic approach, we determine two distinct regimes in the
heating dynamics. While the NFL heats exponentially and thermalizes rapidly, we
report that the presence of quasi-particles in the heavy FL obstructs heating
and thermalization over comparatively long time scales. Prethermal
high-frequency dynamics and possible experimental realizations of
non-equilibrium SYK physics are discussed as well.
