The exploration of two-dimensional (2D) materials with exceptional physical and chemical properties is essential for the advancement of solar water splitting technologies. However, the discovery of 2D materials is currently heavily reliant on fragmented studies with limited opportunities for fine-tuning the chemical composition and electronic features of compounds. Starting from the V2DB digital library as a resource of 2D materials, we set up and execute a funnel approach that incorporates multiple screening steps to uncover potential candidates for photocatalytic water splitting. The initial screening step is based upon machine learning (ML) predicted properties, and subsequent steps involve first-principles modeling of increasing complexity, going from density functional theory (DFT) to hybrid-DFT to GW calculations. Ensuring that at each stage more complex calculations are only applied to the most promising candidates, our study introduces an effective screening methodology that may serve as a model for accelerating 2D materials discovery within a large chemical space. Our screening process yields a selection of 11 promising 2D photocatalysts.