The application of Gen AI (Generative AI) across multiple sectors like manufacturing and service domains, shows transformative effects to improve socially responsible decision-making and collaborative efforts. Yet it remains insufficiently investigated in the context of a socially responsible supply chain (SRSC) towards sustainable supply chain management (SSCM) in a wider context. Gen AI enables faster reporting and adaptive responses to enhance decision-making, which together improve supply chain flexibility while promoting social responsibility. Although previous research recognizes Gen AI's contribution to social functionality within a supply chain, it does not provide a full theoretical structure for analyzing how Gen AI solutions develop and function in SSCM. Prior research stresses the importance of making people and communities central elements in SSCM from the outset. To address this gap, this research conducts a rigorous qualitative study by analyzing 82 exemplary SSCM cases from manufacturing and service sectors through content analysis. The research explores how organizations can leverage dynamic capability theory (DCT) to adopt and integrate Gen AI systems. The findings demonstrate the stakeholder role in SSCM: 1) NGOs and universities provide essential knowledge and skills together with resources which support sustainable practices; 2) active collaboration with external stakeholders creates competitive benefits while promoting wider implementation of sustainability efforts through imitation. This research delivers a conceptual framework, showing how dynamic supply chain capabilities enabled by Gen AI affect stakeholder alignment towards sustainability goals while mobilizing stakeholders towards SSCM practices; this creates positive effects for wider communities in dynamically evolving Gen AI based SC systems. Our study utilizes micro-foundations of dynamic capabilities to deliver actionable recommendations for managers and outlines future research paths for expanding sustainability practices across multiple dimensions using Gen AI. This study provides helpful insights for professionals, researchers, and leaders to achieve Sustainable Development Goals (SDGs).