  We present a comprehensive investigation of the light-matter interaction
dynamics in two-dimensional materials coupled with a spectrally isolated cavity
mode in the strong coupling regime. The interaction between light and matter
breaks the translational symmetry of excitons in the two-dimensional lattice
and results in the emergence of a localized polariton state. Employing a novel
approach involving transformation to exciton reaction coordinates, we derive a
Markovian master equation to describe the formation of a macroscopic population
in the localized polariton state. Our study shows that the construction of a
large-scale polariton population is affected by correction terms addressing the
breakdown of translational symmetry. Increasing the spatial width of the cavity
mode increases the Coulomb scattering rates while the correction terms saturate
and affect the system's dynamics progressively less. Tuning the lattice
temperature can induce bistability and hysteresis with different origins than
those recognized for quantum wells in larger microcavities. We identify a limit
temperature $T_{\mathrm{l}}$ as a key factor for stimulated emissions and
forming a macroscopic population, enriching our understanding of strong
coupling dynamics in systems with extreme confinement.
