As the concept of corporate social responsibility advances, it is crucial to recognize the broad roles of sustainability and the Sustainable Development Goals (SDGs) influencing the implementation of corporate social responsibility (CSR) initiatives. This research contributes to the expanding field of CSR, sustainable innovation ambidexterity (SIA), sustainable supply chain management (SSCM), and second-order social capital (SOSC). This research produced a theoretical framework based on social exchange theory, social capital theory, and Carroll’s CSP model to investigate the impact of CSR on SIA, SSCM, and SOSC. Furthermore, this study examined the mediating effects of SSCM and SOSC on the correlation between CSR and SIA. Additionally, this study presents a model to explain the impact of SSCM and SOSC on SIA. This study concentrated on top-level managers of several manufacturing businesses situated in Pakistan. A total of 42 manufacturing businesses were chosen utilizing a convenience cluster sampling method. As per the results of this research, CSR was discovered to have a positive impact on SSCM, SIA, and, SOSC. Moreover, SOSC and SSCM were found to be in a significant relationship with SIA. Finally, SOSC and SSCM fully mediated the relationship between CSR and sustainable innovation ambidexterity. This research can guide companies by effectively delivering their finances in CSR initiatives. The findings also suggest that companies should concentrate on improving their CSR initiatives because CSR has a significant effect on SIA. The SDGs provide a road map for companies that can assist them to tactically manage their CSR initiatives according to the international and national sustainable development guidelines. Hence, the CSR–SDG tie is essential for the improvement in the role of CSR in sustainable development. Moreover, to improve and measure SSCM, SOSC, and SIA, policymakers and general managers should devote efforts to CSR.