In this talk, I will report on our numerical lattice simulations of partons traversing the boost-invariant, non-perturbative glasma as created at the early stages of collisions at RHIC and LHC . Since these highly energetic partons are produced from hard scatterings during heavy ion collisions, they are already affected by the first stage of the medium's time evolution, the glasma, which is the pre-equilibrium precursor state of the quark-gluon plasma. We find that partons quickly accumulate transverse momentum up to the saturation momentum during the glasma stage. Moreover, we observe an interesting anisotropy in transverse momentum broadening of partons with larger broadening in the rapidity than in the azimuthal direction. Its origin can be related to correlations among the longitudinal color-electric and color-magnetic flux tubes in the initial state of the glasma. I will compare these observations to the semi-analytic results  obtained by a weak-field approximation, where we also find such an anisotropy in a parton's transverse momentum broadening.
 A. Ipp, D. I. Müller, D. Schuh, Phys. Lett. B 810 (2020), arXiv:2009.14206
 A. Ipp, D. I. Müller, D. Schuh, Phys. Rev. D 102 (2020), arXiv:2001.10001