We demonstrate the emergence of a non-equilibrium superradiant phase
in the dissipative Rabi-Dicke model. This phase is characterized by a
photonic steady state that oscillates with a frequency close to the
cavity frequency, in contrast to the constant photonic steady state of
the equilibrium superradiant phase in the Dicke model. We relate this
superradiant phase to the population inversion of Floquet states by
introducing a Schwinger representation of the driven two-level systems
in the cavity. This inversion is depleted near Floquet energies that are
resonant with the cavity frequency to sustain a coherent light-field. In
particular, our model applies to solids within a two-band approximation,
in which the electrons act as Schwinger fermions. We propose to use this
Floquet-assisted superradiant phase to obtain controllable optical gain
for a laser-like operation.