We investigate the non-equilibrium dynamics of a resonant level model coupled to a strongly interacting electron bath modeled by a Sachdev-Ye-Kitaev (SYK) model. Different from the well-investigated case of a structureless non-interacting Fermi gas bath leading to a temperature-independent exponential decay of the impurity orbital occupation, we find a temperature-dependent oscillatory decay. We attribute this difference to the lack of quasiparticles in the SYK model, which is reflected in its singular density of states at the Fermi level. Our results are exact and can be obtained analytically by mapping to a suitably structured Fermi gas bath as an ancillary model for the SYK bath.