  Polariton condensation relies on the macroscopic occupation of the
lowest-energy polariton state beyond a critical density. The mechanisms driving
the occupation and depopulation of this state all rely on multi-particle
scattering, whose dynamics determine the extent to which condensates can form
spontaneously. To pinpoint many-body processes hindering polariton condensation
in two-dimensional metal-halide semiconductors, we examine the
exciton-polariton dynamics in a Fabry-P\'erot microcavity over timescales
involving polariton ($\bm{\ll 1}$\,ps) and exciton scattering ($\bm{\gg
1}$\,ps). We find enhanced nonlinear exciton-exciton interactions in the
microcavity versus the bare semiconductor and ultrafast polariton scattering
depopulating the lowest-energy polariton state. We posit that the complex
scattering landscape between the exciton reservoir and polaritons limits the
formation of polariton condensates in these semiconductors, and we discuss the
generality of our conclusions for highly polar materials in which the lattice
mediates multi-particle correlations.
