Enhancing the dynamic properties of expansive soils using cementitious materials has attracted the attention of many researchers over the past few decades. Supplementary cementitious materials (SCMs) can be used as partial substitute for cement owing to their pozzolanic activity which further improves the mechanical performance of cement-stabilized soils upon curing. In this study, the effect of cement and zeolite incorporation on the mechanical behavior of expansive clay was quantified using the pressure wave velocity (Vp) indicator obtained from ultrasonic pulse velocity tests performed at different curing times. Furthermore, a polynomial model was developed to establish the relationship between Vp and zeolite replacement levels at specific curing times and cement contents. The results show that a polynomial function captured the decreasing trend of Vp upon the increase in zeolite at curing times below 14 days. Additionally, the developed equation explained the upward trend of Vp owing to the pozzolanic activity of zeolite at later curing times with an accuracy of over 92%. The coefficients of the polynomial model also increased with the increment of the cement percentage which conformed to the consecutive rise in Vp. Ultimately, the polynomial coefficients were expressed in terms of cement content and curing time using the Volterra series. Using this model, the optimum percentage of cement replaced with zeolite (Zopt), the efficiency of using Zopt instead of cement, and the percentage of zeolite replacement to achieve equivalent Vp of cemented clay samples (ZC) were estimated. The findings of this study contribute to promoting geotechnical sustainability by replacing cement with zeolite which has a considerably lower environmental footprint.