This study investigated the combined effects of calcium carbide waste (CCW) and lateritic soil (LS) on sustainable concrete’s fresh and mechanical properties as a construction material for infrastructure development. The study will explore the possibility of using easily accessible materials, such as lateritic soils and calcium carbide waste. Therefore, laterite soil was used to replace some portions of fine aggregate at 0% to 40% (interval of 10%) by weight, while CCW substituted the cement content at 0%, 5%, 10%, 15%, and 20% by weight. A response surface methodology/central composite design (RSM/CCD) tool was applied to design and develop statistical models for predicting and optimizing the properties of the sustainable concrete. The LS and CCW were input variables, and compressive strength and splitting tensile properties are response variables. The results indicated that the combined effects of CCW and LS improve workability by 18.2% compared to the control mixture. Regarding the mechanical properties, the synergic effects of CCW as a cementitious material and LS as a fine aggregate have improved the concrete’s compressive and splitting tensile strengths. The contribution of LS is more pronounced than that of CCW. The established models have successfully predicted the mechanical behavior and fresh properties of sustainable concrete utilizing LS and CCW as the independent variables with high accuracy. The optimized responses can be achieved with 15% CCW and 10% lateritic soil as a substitute for fine aggregate weight. These optimization outcomes produced the most robust possible results, with a desirability of 81.3%.