Steel-concrete-steel (SCS) sandwich structures consist of two steel faceplates and a concrete core, interconnected through mechanical SHEAR connectors to form an integrated composite system. Among various SHEAR connectors, BOX-profile (BP) SHEAR connectors have demonstrated superior SHEAR strength. Despite this, no equation has been developed to estimate the SHEAR strength of BP SHEAR connectors, unlike the well-established provisions for stud-bolt connectors. This study aims to address this gap by proposing a predictive equation for the SHEAR strength of BP SHEAR connectors using the Taguchi design of experiments (DOE). Key parameters, including the thickness, width, and yield strength of BP SHEAR connectors, as well as the thickness and compressive strength of the concrete core, were systematically analyzed. A total of 32 specimens were designed, and their behavior was validated through experimental push-out TESTs and simulations, focusing on failure modes and load-slip curves. Finite element (FE) analysis and gene expression programming (GEP) were employed to develop a predictive equation incorporating two failure modes: concrete failure and BP failure. The proposed equation was rigorously evaluated against existing code provisions using statistical metrics such as root-mean-square error (RMSE), mean absolute percentage error (MAPE), and Nash-Sutcliffe efficiency (NSE). Results demonstrated the superior accuracy and reliability of the proposed model. This study provides a robust framework for designing BP SHEAR connectors, addressing a critical gap in the design of SCS sandwich structures and advancing their practical application.