Transition metal dichalcogenide (TMD) monolayers (1L) have been established as important building blocks for quantum materials. Hybridization between light and matter states, in particular in plasmonic nanostructures, offers great opportunities to tailor their optical and electronic properties on the nanoscale. To probe and distinguish ubiquitous coherent and incoherent energy transfer processes, ultrafast two-dimensional electronic spectroscopy (2DES) has proven to be a valuable tool. Here, we investigate a hybrid plasmonic nanostructure comprised of 1L-WS2 placed on a periodic silver nano-slit array using ultrafast 2DES with 10-fs time resolution. We observe a 20-fold increase of the optical nonlinearity of the polaritonic system compared to bare 1L-WS2 and ultrafast 2DES dynamics during the dephasing time (~50 fs). We model our nonlinear spectra using a three-oscillator model that accounts both for far field coupling of the plasmon to momentum bright excitons and near field couplings to momentum dark excitons of the TMD and consider Pauli blocking and excitation-induced dephasing as the main origins for the optical nonlinearity. This allows us to explain our experimental data as a transfer from coherent polaritons at early times to incoherent polaritons and dark state populations within ~50 fs. Our findings highlight the important role of many-body interactions and dark states in the collective response of TMD-based polariton systems.