We compute the heavy quark momentum diffusion coefficient using effective kinetic theory for a system going through bottom-up isotropization until approximate hydrodynamization. We find that when comparing the nonthermal diffusion coefficient to the thermal one for the same energy density, the observed deviations throughout the whole evolution are within 30\% from the thermal value. For thermal systems matched to other quantities we observe considerably larger deviations. We also observe that the diffusion coefficient in the transverse direction dominates at large occupation number, whereas for an underoccupied system the longitudinal diffusion coefficient dominates. Similarly, we study the jet quenching parameter, where we obtain a smooth evolution connecting the large values of the glasma phase with the smaller values in the hydrodynamical regime.