In light of growing global concerns for sustainable development and environmental protection, green supply chain finance has emerged as a promising approach to promoting environmentally responsible business practices. This paper examines the structure of the green supply chain finance credit market under government regulation and constructs a tripartite evolutionary game model involving green small and medium enterprises (SMEs), core enterprises, and financial institutions. Through analysis of game equilibrium points and numerical simulation, this study investigates the impact of initial conditions on evolutionary trajectories. Results indicate that the initial proportion of positive strategies adopted by game participants affects the system‘s evolutionary trajectories. A higher initial proportion of positive strategies facilitates achieving credit business in green supply chain finance. Increasing government regulation punishment values can help achieve credit business and stabilize the credit market. Cost factors are negatively correlated with the game system‘s evolution direction. Reducing admission costs for SMEs, evaluation costs for core enterprises, and evaluation and supervision costs for financial institutions can effectively promote convergence to a Pareto optimal state.