Precisely grasping the spatial correlation network characteristics of regional green total factor productivity, exploring its dynamic evolutionary mechanisms, and accurately identifying the most effective paths for enhancing and sustaining regional green total factor productivity are crucial to achieve sustainable and high-quality regional economic development. This study employs social network analysis to meticulously analyze the spatial correlation features of green total factor productivity across China's 30 provinces from 2006 to 2021, systematically investigating the formation mechanisms and evolutionary dynamics of provincial green total factor productivity spatial correlation networks through temporal dependency analysis and network structure decomposition. Utilizing the temporal exponential random graph model (TERGM), the research elucidates multi-scale interactions among market forces, policy interventions, and geographic constraints, aiming to identify trend drivers and quantify synergistic effects in comprehensive green transformation. The results show that: (1) Provincial green total factor productivity is on an upward trajectory, yet it displays pronounced spatial disparities, with a distinct hierarchical pattern emerging where the Eastern regions outperform the Central, which in turn surpass the Western regions. The persistent Matthew effect has progressively widened the development gap between the prosperous Eastern and the less developed Western regions. (2) Inter-provincial cooperation and correlation in green total factor productivity have transcended geographical proximity. The exploration unveils that, despite the intricate, multi-dimensional, and diverse structural characteristics inherent in the spatial correlation network of provincial green total factor productivity, the strikingly evident core-periphery structure serves as a clear indication of the unfinished development and incomplete establishment of a seamless and efficient factor transmission pathway. (3) By employing modular analysis to segment the entire region into four distinct plates, it becomes apparent that development is markedly uneven, with notably sparse internal connections. This suggests that there is considerable scope for enhancing and deepening inter-provincial collaborations. Among these plates, the "net beneficiary" segment, primarily led by Beijing, Tianjin, and Shanghai, demonstrates a pronounced siphon effect that overshadows its radiation effect, thereby emphasizing their prominent and influential position. On the other hand, the "net spillover" regions, encompassing Inner Mongolia, Heilongjiang, and Qinghai, exhibit substantial spillover effects, indicating a significant untapped potential for green development that necessitates stimulation and cultivation to fully harness their capabilities. (4) The TERGM results indicate that the formation and evolution of China's spatial correlation network for green total factor productivity are influenced by many factors, including market dynamics, government policies, and geographic proximity. To mitigate regional disparities in green total factor productivity growth and expedite the comprehensive green transformation of economic and social development, it is imperative to harness the synergistic effects of multiple stakeholders, factors, and connections. This underscores the need for a holistic approach integrating various entities and elements to foster a more equitable and sustainable green development path.