  We show how a driven-dissipative cavity coupled to a collective ensemble of
atoms can dynamically generate metrologically useful spin-squeezed states. In
contrast to other dissipative approaches, we do not rely on complex engineered
dissipation or input states, nor do we require tuning the system to a critical
point. Instead, we utilize a strong symmetry, a special type of symmetry that
can occur in open quantum systems and emerges naturally in systems with
collective dissipation, such as superradiance. This symmetry preserves
coherence and allows for the accumulation of an atom number-dependent Berry
phase which in turn creates spin-squeezed states via emergent one-axis twisting
dynamics. This work shows that it is possible to generate entanglement in an
atom-cavity resonant regime with macroscopic optical excitations of the system,
going beyond the typical dispersive regime with negligible optical excitations
often utilized in current cavity QED experiments.
