We study jet momentum broadening in heavy-ion collisions at anisotropic initial stages with focus on the jet quenching parameter $\hat q$, which we extract using effective kinetic theory. We obtain its non-equilibrium properties during the bottom-up thermalization scenario in a Bjorken-expanding plasma with non-thermal anisotropic initial conditions. By studying the time-dependence of the momentum broadening we find that q^ along the beam axis is suppressed compared to the transverse plane during the overoccupied phase, and enhanced during the underoccupied phase.