  We report the observation of long-lived Floquet prethermal states in a bulk
solid composed of dipolar-coupled $^{13}$C nuclei in diamond at room
temperature. For precessing nuclear spins prepared in an initial transverse
state, we demonstrate pulsed spin-lock Floquet control that prevents their
decay over multiple-minute long periods. We observe Floquet prethermal
lifetimes $T_2'\approx$90.9s, extended >60,000-fold over the nuclear free
induction decay times. The spins themselves are continuously interrogated for
$\sim$10min, corresponding to the application of $\approx$5.8M control pulses.
The $^{13}$C nuclei are optically hyperpolarized by lattice Nitrogen Vacancy
(NV) centers; the combination of hyperpolarization and continuous spin readout
yields significant signal-to-noise in the measurements. This allows probing the
Floquet thermalization dynamics with unprecedented clarity. We identify four
characteristic regimes of the thermalization process, discerning short-time
transient processes leading to the prethermal plateau, and long-time system
heating towards infinite temperature. This work points to new opportunities
possible via Floquet control in networks of dilute, randomly distributed,
low-sensitivity nuclei. In particular, the combination of minutes-long
prethermal lifetimes and continuous spin interrogation opens avenues for
quantum sensors constructed from hyperpolarized Floquet prethermal nuclei.
