This paper addresses critical gaps in artificial intelligence (AI) value alignment research concerning historically marginalized communities in the Global South, with a specific focus on Dalits and Adivasis in India. We propose a multidimensional approach that integrates B.R. Ambedkar's and Amartya Sen's theoretical frameworks on social justice with Clifford Geertz's thick description methodology to develop context-sensitive norm elicitation processes. By examining how deeply entrenched sociopolitical hierarchies influence these communities' agency to process and express information about their own values, we demonstrate that conventional approaches to value alignment inadequately address the unique challenges faced by these communities. Our framework emphasizes the role of Indian AI missions in creating culturally relevant scenarios for norm elicitation, ensuring meaningful participation of marginalized communities in AI alignment processes. This approach not only advances the discourse on inclusive AI development but also provides practical strategies for implementing value alignment methodologies that acknowledge and address historical power dynamics.