The early stages of relativistic heavy-ion collisions involve a non-thermal gluonic plasma with high occupancy. We examine how the broad quasiparticle excitation characteristics found in an earlier study for such a 2+1 dimensional system affect the heavy quark diffusion coefficient. We show that essential transport properties can be extracted from gauge-fixed quantities, accurately reproducing the time evolution of the gauge-invariant coefficient. Notably, we identify a novel transport peak in the low-frequency spectrum that is crucial for the correct reproduction. Additionally, we draw parallels to features observed in the Glasma, indicating significant implications for its transport properties.