S-adenosyl-L-methionine (SAM) is a substrate for many enzyme-catalyzed reactions and provides methyl groups in numerous biological methylations, and thus has vast applications in the medical field. Saccharomyces cerevisiae has been engineered as a platform with significant potential for producing SAM, although the current production has room for improvement. To surpass the restriction, a series of metabolic engineering strategies were employed to enhance the synthesis of SAM in this study. These strategies included enhancing SAM synthesis by overexpression of SAM2, met6, and str2, increasing ATP supply by integration of adkI and PYC, and down-regulating SAM metabolism by disrupting erg4 and erg6 and replacing the original promoter of CYS4 with a weaker promoter. After combinatorial metabolic engineering, Bayesian optimization was conducted on the obtained strain C262P6 to optimize the fermentation medium. A final yield of 2972.8 mg/L at 36 h with 29.7% of the L-Met conversion rate in the shake flask was achieved, which was 26.3 times higher than that of its parent strain and the highest reported production in the shake flask to date. This paper establishes a feasible foundation for the construction of SAM-produced strains using metabolic engineering strategies and demonstrates the effectiveness of Bayesian optimization in optimizing fermentation medium to enhance the generation of SAM.