Enhancing the sustainable development capability of new public cultural spaces is a key measure to promote the high-quality development of public cultural services. Exploring the capability dimensions and conditional configurations of the sustainable development of new public cultural spaces can provide important theoretical references for their efficient operation. By comprehensively applying meta-synthesis analysis and qualitative comparative analysis, 114 high-quality sample literatures were selected from mainstream domestic and foreign databases. Through coding, extraction, and synthesis, the MCSI model for the sustainable development capability of new public cultural spaces was constructed. Using fuzzy-set qualitative comparative analysis (fsQCA), based on 40 cases of new public cultural spaces, the configuration paths for improving their sustainable development capability were identified. The study found that the sustainable development capability of new public cultural spaces includes four interrelated dimensions: Management, Collaboration, Service, and Innovation. The key combination paths for enhancing such capability are innovation-driven, management-led, service-integrated, and efficiency-improving. On the basis of these findings, enlightenment reflections are put forward in terms of focusing on advantageous resources to build distinctive brands, deepening service functions to respond to cultural needs, and establishing a collaborative foundation to integrate cross-sector resources.