The dynamics of charge carriers in disordered organic semiconductors is inherently difficult to probe by spectroscopic methods. Thermally stimulated luminescence (TSL) is an approach that detects the luminescence resulting from the recombination of spatially-well-separated geminate charge pairs, usually at low temperature. In this way, the density of states (DOS) for charges can be determined. In this study, we demonstrate that TSL can also be used for probing an occupied density of states formed by a low-temperature energetic relaxation of photogenerated charges. Another approach used to gain an insight into the charge-relaxation process is kinetic Monte Carlo (KMC) simulations. Here, we use both techniques to determine the energetic distribution of charges at low temperatures. We find that the charge dynamics is frustrated, yet this frustration can be overcome in TSL by using an infrared (IR) push pulse, and in KMC simulations by a long simulation time that allows for long-range tunneling. Applying the IR-push TSL to pristine amorphous films of 18 commonly used low-molecular-weight organic light-emitting diode materials, we find that the width of the occupied DOS amounts to about 2/3 of the available DOS. The same result is obtained in KMC simulations that consider spatial correlations between site energies. Without the explicit consideration of energetic correlations, the experimental values cannot be reproduced, which testifies to the importance of spatial correlations for charges.