  Time- and angle-resolved photoemission spectroscopy (tr-ARPES) constitutes a
powerful tool to inspect the dynamics and thermalization of hot carriers. The
identification of the processes that drive the dynamics, however, is
challenging even for the simplest systems owing to the coexistence of several
relaxation mechanisms. Here, we devise a Green's function formalism for
predicting the tr-ARPES spectral function and establish the origin of carrier
thermalization entirely from first principles. The predictive power of this
approach is demonstrated by an excellent agreement with experiments for
graphene over time scales ranging from a few tens of femtoseconds up to several
picoseconds. Our work provides compelling evidence of a non-equilibrium
dynamics dominated by the establishment of a hot-phonon regime.
