  Electron dynamics at weakly bound interfaces of organic/inorganic materials
are easily influenced by large-amplitude nuclear motion. In this work, we
investigate the effects of different approximations to the equilibrium nuclear
distributions on the ultrafast charge-carrier dynamics of a laser-excited
hybrid organic/inorganic interface. By considering a prototypical system
consisting of pyrene physisorbed on a MoSe$_2$ monolayer, we analyze linear
absorption spectra, electronic density currents, and charge-transfer dynamics
induced by a femtosecond pulse in resonance with the frontier-orbital
transition in the molecule. The calculations are based on \textit{ab initio}
molecular dynamics with classical and quantum thermostats, followed by
time-dependent density-functional theory coupled to multi-trajectory Ehrenfest
dynamics. We impinge the system with a femtosecond (fs) pulse of a few hundred
GW/cm$^2$ intensity and propagate it for 100 fs. We find that the optical
spectrum is insensitive to different nuclear distributions in the energy range
dominated by the excitations localized on the monolayer. The pyrene resonance,
in contrast, shows a small blue shift at finite temperatures, hinting at an
electron-phonon-induced vibrational-level renormalization. The electronic
current density following the excitation is affected by classical and quantum
nuclear sampling through suppression of beating patterns and faster decay
times. Interestingly, finite temperature leads to a longer stability of the
ultrafast charge transfer after excitation. Overall, the results show that the
ultrafast charge-carrier dynamics are dominated by electronic rather than by
nuclear effects at the field strengths and time scales considered in this work.
