The quaternary compound Cu2BaSnS4 (CBTS) has emerged as a suitable and attractive light-harvesting material due to its promising optoelectronic features as well as nontoxic and low-cost constituent elements. Yet efficiency of CBTS-based solar cells did not reach the Shockley-Queisser limit. Here, what we believe to be a novel structure ITO/WO3/CBTS heterojunction solar cell is designed and modeled using a solar cell capacitance simulator in one-dimension (SCAPS-1D). In this work, a what we also believe to be a novel WO3 as a buffer layer is proposed for the first time for the efficiency enhancement of CBTS thin film solar cells. Numerical investigation of the performance of CBTS-based solar cells without and with cuprous oxide (Cu2O) back surface field (BSF) is explored. The impact of thickness, doping density, bulk, and interface defect density of an absorber, buffer and window layer, working temperature, shunt and series resistance, back contact work function, and back surface recombination velocity were analyzed and optimized without and with the BSF layer. In this work, the optimized solar cell achieved an efficiency of 18.8%, fill factor (FF) of 83.79%, short-circuit current density (JSC) of 15.99 mA/cm2, and open circuit voltage (VOC) of 1.4 V without Cu2O BSF layer at optimal CBTS absorber and WO3 buffer layer thickness of 2 µm and 0.04 µm respectively. Furthermore, the efficiency boosted to 21.12% with VOC of 1.43 V, JSC of 16.8 mA/cm2 and FF of 87.77% by inserting 0.1 µm Cu2O BSF layer. Therefore, these results will facilitate the fabrication of an efficient and low-cost CBTS-based solar cell with promising WO3 and Cu2O as buffer and BSF layer, respectively.