In the idealized high-energy limit of heavy-ion collisions, the system right after a collision is described as an over-occupied gluonic plasma expanding in the longitudinal direction. The understanding of the quark dynamics in such a pre-equilibrium state is of prime importance since it has a direct connection to electromagnetic probes. We report on a numerical study of the Boltzmann equation including two-to-two scatterings of gluons and quarks in the expanding geometry. In the gluon sector, we confirm the self-similar scaling behavior of the one-particle momentum distribution that is consistent with the bottom-up thermalization scenario. Also in the quark sector, we find that the distribution function show scaling behavior like those of gluons.