This study, grounded in the stimulus-organism-response (SOR) theory, aims to explore how stimulus factors (school support) influence cognitive organisms (psychological resilience, self-efficacy, attitude toward AI, and acceptance of AI), which in turn enhance behavioral responses (AI literacy), while also examining the detrimental effects of AI anxiety. A cross-sectional design was employed, utilizing sample data from 1,518 teachers. The results of PLS-SEM indicate that school support exerts a significant positive impact on psychological resilience, self-efficacy, attitude toward AI, and acceptance of AI. These cognitive factors, in turn, significantly enhance AI literacy. However, while AI anxiety negatively affects these cognitive factors, it does not exhibit a significant direct impact on AI literacy. Additionally, the study reveals the mediating roles of psychological resilience, self-efficacy, attitude toward AI, and acceptance of AI in the relationship between school support and AI literacy. The findings of fsQCA identify five high-level configurational pathways and one non-high-level pathway, demonstrating an asymmetric relationship between these configurations. The consistency values of all six pathways exceed 0.9, indicating that these configurations are sufficient conditions influencing teachers' AI literacy. This study provides a theoretical framework for analyzing factors affecting teachers' AI literacy and offers practical guidance for policy interventions and innovative practices to enhance teachers' AI literacy.