  Time-resolved soft-X-ray photoemission spectroscopy is used to simultaneously
measure the ultrafast dynamics of core-level spectral functions and excited
states upon excitation of excitons in WSe$_2$. We present a many-body
approximation for the Green's function, which excellently describes the
transient core-hole spectral function. The relative dynamics of excited-state
signal and core levels reveals a delayed core-hole renormalization due to
screening by excited quasi-free carriers, revealing an excitonic Mott
transition. These findings establish time-resolved core-level photoelectron
spectroscopy as a sensitive probe of subtle electronic many-body interactions
and an ultrafast electronic phase transition.
