Depth-resolved measurements of the two-dimensional angular correlation of annihilation radiation (2D-ACAR) were performed at the high-intensity slow-positron beam of Lawrence Livermore National Laboratory. We studied the formation of positronium in thin films of methylsilsesquioxane (MSSQ) spin-on glass containing open-volume defects in the size of voids. Samples with different average void sizes were investigated and positronium formation could be found in all cases. The width of the angular correlation related to the annihilation of parapositronium increased with the void size indicating the annihilation of non-thermalized parapositronium.