Optimizing the Job Shop Scheduling Problem (JSP) is critical to minimizing makespan and enhancing operational efficiency within contemporary manufacturing environments aligned with Industry 4.0 and ESG sustainability goals. Existing methods encounter challenges such as premature convergence in Genetic Algorithms (GA), scalability issues in Memetic Algorithms (MA), inefficient exploration in Random Walk (RW), and high computational requirements of Message Passing Neural Networks (MPNN). To overcome these limitations, this study proposes a hybrid optimization framework combining the effective search capabilities of MA and the advanced graph-based modeling strengths of MPNN. The integrated method significantly improves solution accuracy, convergence speed, and diversity while reducing idle time, energy usage, and carbon emissions. Consequently, it supports sustainable manufacturing and compliance with international standards like the EU Carbon Border Adjustment Mechanism (CBAM), enhancing industrial competitiveness.