Artificial intelligence (AI) is reshaping higher education by changing how students access knowledge, complete academic tasks and engage in innovation. At the same time, unequal access to AI-related competencies may reproduce existing educational inequalities, which raises important concerns for Sustainable Development Goal 4 (SDG 4). Drawing on cultural capital theory and research on digital inequality, this study examines whether family cultural capital is associated with university students’ innovative capacity through AI literacy. In this study, AI literacy is defined as students’ ability to understand, evaluate and use AI critically and responsibly across different contexts. Survey data were collected from 1020 Chinese university students and analyzed using structural equation modeling (SEM) with split-sample validation. The results indicated that family cultural capital remained significantly associated with innovative capacity although its two dimensions operated differently. Cultural resources had a significant direct effect on innovative capacity and also positively predicted technical application skills but not awareness of the social impact of AI. Embodied cultural capital did not have a significant direct effect on innovative capacity, but its total effect was significant, and it positively predicted both dimensions of AI literacy. Mediation analysis further showed that technical application skills significantly mediated the relationship between both dimensions of family cultural capital and innovative capacity, whereas awareness of the social impact of AI did not show a significant mediating effect. These findings suggest that family cultural capital continues to matter in the AI era not only through direct advantage but also through its conversion into AI-related competencies. The study highlights the need for higher education institutions to strengthen equitable support for practical AI capability development in order to promote inclusive innovation and advance SDG 4.