This theoretical study rigorously investigates how generative artificial intelligence reshapes decision-making in social entrepreneurship by modeling the opportunity search process through the lens of optimal stopping theory. Social entrepreneurs often face high uncertainty and resource constraints, requiring them to strategically balance the cost of continued searching with the chance of identifying socially impactful opportunities. This study develops a formal model that captures two core mechanisms of generative AI: reducing search costs and increasing the probability of mission-aligned opportunity success. The theoretical analysis yields three key findings. First, generative AI accelerates the optimal stopping point, allowing social entrepreneurs to act more quickly on high-potential opportunities by lowering cognitive and resource burdens. Second, the influence of increased success probability outweighs that of reduced search costs, underscoring the strategic importance of insight quality over efficiency in socially embedded contexts. Third, the benefits of generative AI are amplified in uncertain environments, where it helps navigate complexity and mitigate information asymmetry. These insights contribute to a deeper conceptual understanding of how intelligent technologies transform the cognitive and strategic dimensions of social entrepreneurship, and they offer empirically testable propositions for future research at the intersection of AI, innovation, and mission-driven opportunity pursuit.