Upon the implementation of the European Union Carbon Border Adjustment Mechanism (CBAM), substantial challenges are anticipated to impact the international trade of Chinese steel products. To safeguard the competitiveness of Chinese steel products on the global stage, this paper establishes a tripartite evolutionary game model, involving large steel enterprises, small and medium-sized steel enterprises, and the government. The model integrates collaborative emission reduction and free-riding benefits among enterprises, along with the government's dynamic subsidies and penalties. The paper analyzes the evolutionary trends and stable states of the three parties during different stages of CBAM, including a sensitivity analysis of key parameters. The findings indicate that large enterprises demonstrate a heightened sensitivity to CBAM, while small and medium-sized enterprises are more significantly influenced by free-riding benefits. Government intervention should be strategically timed and incline towards passive management during the strengthening phase of CBAM. Additionally, the refinement of the Chinese carbon market emerges as an effective means to counter CBAM. This paper provides theoretical support for how steel enterprises and the government can respond to CBAM, aiding stakeholders in selecting optimal strategies during different implementation stages and mitigating the impacts of CBAM to the maximum extent possible.