The molecular makeup of the Interstellar Medium (ISM) holds the key to tracing the pathways that lead to star- and planet-forming regions, including our own. In dense molecular clouds, chemical complexity flourishes on the surfaces of cold dust grains, which act as catalytic sites that enable the formation of icy mantles containing molecules like water (H2O), methane (CH4), and ammonia (NH3), as well as interstellar Complex Organic Molecules (iCOMs). However, the precise formation mechanisms for iCOMs, particularly sulfur-bearing carriers in the solid state, remain elusive. In this study, we experimentally investigate the role of atomic carbon in driving solid-state reactions forming S-bearing iCOMs, uncovering new potential pathways for molecular complexity in the ISM. Using the SURFRESIDE3 setup, interstellar ice analogues are grown on a cold (10 K) gold-plated substrate within an ultra-high vacuum (UHV) chamber (P_base = 10^-10 mbar) by the co-deposition atomic (H/D, C) and molecular species (H2S, H2). The ices are monitored via reflection absorption infrared spectroscopy (RAIRS), and analyzed with a quadrupole mass spectrometer (QMS) during temperature-programmed desorption (TPD) measurements. I will discuss the formation pathways of CH3SH and H2CS in prestellar cores and the implications their formation routes have on deuteration ratios and gas-phase abundances found at later stages of star formation.