To foster the sustainable development of culture, particularly focusing on the preservation of cultural heritage, encompassing relics, intangible cultural heritage, and historical sites, China has launched a strategy for the digitalization of culture, with the goal of establishing a holistic national big data framework for cultural resources. To improve the efficiency of collaborative supply of cultural resource big data among various parties and to further advance the sustainable development of culture, this research has created a cooperative model that includes cultural institutions, a cultural resource big data service platform, and government participation. Our research findings, based on prospect theory and evolutionary game theory combined with Chinese practice, are presented below. (1) Various factors, including the coefficient of digital infrastructure empowerment, access charges for digital infrastructure, government penalties, and the probability of data leakage, have varying effects on the system in different states. (2) Once the industry has developed, the government can increase the impact of digital infrastructure empowerment to create stronger incentives, rather than relying solely on rewards or penalties. (3) When the value level of cultural resource big data is high, the benefit distribution coefficient does not affect the system evolution results. Finally, we offer practical insights for the government, cultural organizations, and cultural resource big data service platforms based on our research results. Our research offers Chinese insights for global cultural sustainable development.