The compression effects on the thermoelastic and thermodynamic properties of cubic zincblende silicon–tin alloy (SiSn) were explored using a multi-methodological approach, deploying data mining methods, theoretical equation-of-state parameters, and the Quasi-Harmonic Debye Model. We analyze the relative volume, isothermal bulk modulus, thermal expansion coefficient, Debye temperature, sound velocity, and microhardness of the SiSn compound under pressures up to 8 GPa. The study commences with the data mining-based searches for a structural model and continues with an analysis of the pressure dependence of the relative volume using the Vinet equation of state, followed by an investigation of the bulk modulus and other related thermoelastic properties. Moreover, the variation of microhardness with temperature is predicted, demonstrating a patent progressive decline as the temperature rises from 0 to 800 K. The thermodynamic properties of the SiSn compound have been explored using the quasi-harmonic Debye model in temperatures ranging from 0 to 800 K and pressures ranging from 0 to 8 GPa, respectively. In addition to the information not found in the literature and offered by this study, our work also establishes a simplified model that can predict the evolution of microhardness as a function of temperature, firstly for the SiSn compound, and perhaps can extend to group-IV semiconductors.