The COVID-19 pandemic has severely impacted the global social sustainability of the supply chains, pushing them towards a more flexible management approach. However, there is a paucity of literature that focuses on social sustainability issues for emerging economies. In the post-COVID-19 period, firms around the world will face several critical challenges to social sustainability, which will hinder achieving sustainable development goals (SDGs). Against this backdrop, this study identifies the pressing challenges to social sustainability in the post-COVID-19 context by a literature review and opinions from an expert panel, focusing on the footwear supply chain. In this paper, the best–worst method is applied to compute the criticality of social sustainability challenges towards the flexibility of the supply chains. The study findings reveal that among the nine identified critical challenges, “high level of lay off”, “health protocol development”, “complexity in ensuring workplace safety”, “facing trouble in mental health”, and “lack of government enforcement and regulations for social issues” are reported as the top five challenges, respectively. Furthermore, this study suggests several flexible managerial guidelines, which will help practitioners and policymakers to achieve SDGs considering the COVID-19 pandemic.