Science and technology-driven small and medium-sized enterprises (SMEs) have emerged as vital players in China’s economic landscape, with unlisted SMEs assuming a significant role. However, these unlisted SMEs face formidable financing challenges, exacerbated by information asymmetry and limited access to diverse funding sources. This research introduces a comprehensive Evaluation Indicator System tailored for unlisted science and technology-based SMEs in Province A, China. Grounded in the Catastrophe Progression Method, this system provides an objective and multidimensional assessment of financing capacity, accounting for factors like innovation, growth, solvency, and regional dynamics. Empirical validation demonstrates the system’s practical relevance, reaffirming its potential as a reliable tool for evaluating financing capacity. The study sheds light on the financing stages of these SMEs, emphasizing the importance of external investment channels, especially for growth-stage enterprises. Bank loans remain the primary financing avenue, underscoring the need for enhanced bank evaluation systems. Policymakers should consider tailored approaches based on SME growth stages to optimize resource allocation and support. By addressing the financing challenges faced by unlisted SMEs and fostering a more supportive environment, this research contributes to unlocking their potential for technological innovation, economic growth, and job creation. It underscores the significance of diverse financing options, the role of external factors, and the need for improved bank evaluation processes to facilitate the growth of these enterprises in the dynamic landscape of knowledge-driven economies.