The concrete industry has experienced substantial growth in recent decades, driving increased consumption of natural resources, particularly aggregates and cement. In pursuit of sustainable and cost effective alternatives, overburnt brick aggregates have emerged as a viable substitute. This is particularly relevant in southern India, where extensive brick manufacturing generates not only large volumes of usable bricks but also significant quantities of overburnt brick waste. Typically discarded in landfills, this waste poses environmental challenges; however, recycling it into coarse aggregates—referred to as overburnt brick aggregates (OBB)—offers a sustainable pathway for resource conservation and waste management. This study explores the partial replacement of natural coarse aggregates with OBB in concrete production, in combination with Class C fly ash as a supplementary cementitious material to further enhance sustainability. A series of concrete mixes incorporating varying proportions of OBB and fly ash were prepared and evaluated for mechanical performance. Results indicated that up to 40–50% replacement of natural coarse aggregate with OBB can be achieved without compromising strength, and in some cases, it enhanced both strength and durability. In addition to the experimental program, statistical modeling was conducted to examine the relationships between primary mix design parameters and the compressive strength (CS) of cementitious composites containing cement (C), fly ash (F), fine aggregate (FA), OBB, coarse aggregate (CA), water content (W), and chemical admixtures (A). Pearson’s correlation analysis and Ordinary Least Squares (OLS) regression were applied to quantify parameter interactions and their influence on CS. The correlation heatmap revealed strong multicollinearity among several mix constituents, while regression analysis identified cement, fly ash, and admixture dosage as key predictors of CS. Variance Inflation Factor (VIF) analysis confirmed significant collinearity in FA, C, and OBB, potentially affecting coefficient stability. Residual diagnostics indicated overall model adequacy, with limited influential outliers. These findings provide both experimental and statistical insights to optimize sustainable mix designs incorporating non-conventional aggregates such as OBB.