Two-dimensional (2D) materials have attracted considerable attention due to their remarkable electronic, mechanical and optical properties, making them prime candidates for next-generation electronic and optoelectronic applications. Despite their widespread use in combination with substrates in practical applications, including the fabrication process and final device assembly, computational studies often neglect the effects of substrate interactions for simplicity. In this record, we provide the results of the computational study of the stable 2D molybdenum-sulfur (Mo-S) structures on a c-cut sapphire (Al₂O₃). In particular, we provide the results of the evolutionary search in the Mo-S / Al₂O₃ (0001) system, the machine learning interatomic potential (MLIP) used for local relaxation of the systems during the evolutionary search together with its training set, post-processing data on electronic and phonon band structures of the stable 2D Mo-S structures, and the predicted stability patterns from the perspective of CVD synthesis.