The development of high-performance electron sources requires theoretical frameworks that accurately link the microscopic electronic properties of cathode materials to their macroscopic photoemission observables. Here, we present a many-body extension of the three-step photoemission model for semiconducting photocathodes, directly integrating the GW approximation and the solution of the Bethe-Salpeter equation on top of density functional theory (DFT). This approach overcomes the intrinsic limitations of standard DFT by explicitly accounting for quasiparticle and excitonic effects in the photoexcitation process. The quantum efficiency (QE) is evaluated by combining the ab initio absorption with an emission probability derived as an exciton-weighted average. We validate this model on representative alkali antimonides and demonstrate that a qualitative many-body description successfully captures complex spectral features that empirical models fail to reproduce. Furthermore, by incorporating macroscopic optical effects such as thin-film interference and polarization via Fresnel post-processing, we achieve quantitative agreement with experimental QE values without any adjustment. Minor discrepancies near the photoemission threshold are attributed to the idealized surface barrier adopted in the model and impurity effects in the samples, highlighting specific directions for future refinements. This work establishes a robust, parameter-free ab initio tool that bridges microscopic electronic correlation with macroscopic observables, providing a critical pathway for the rational design of next-generation electron sources.