Reviving traditional knowledge, customs, rituals, and social practices strengthens cultural identity, supports sustainable development, and enhances cultural tourism. Design plays a critical role in making the intangible—such as values, emotions, and meanings—tangible through visual storytelling, environments, and interfaces that highlight cultural narratives. Storytelling fosters community cohesion, identity-building, and intercultural dialogue, encouraging people to coexist harmoniously within diverse societies and natural environments. New technologies contribute to the implementation of storytelling in ICH’s narrative. This paper examines the integration of ICH into higher education through case studies from Greece. Students from two Departments of the University of West Attica, Greece engaged in multidisciplinary projects focusing on lesser-known and UNESCO-listed intangible heritage elements. Over two semesters, 450 case studies all over Greece explored, examined, and visualized cultural narratives through promotional campaigns, using experiential methods and digital tools to convey meaning and raise awareness. The study reveals that engaging students in storytelling-driven design projects cultivates cultural sensitivity, creative thinking, and social responsibility. Academic institutions can become active agents in preserving, revitalizing, and sustaining living traditions, aligning with European values for heritage management. This research contributes to the ongoing dialogue on embedding ICH in university curricula and offers insights for educators, policy makers, and cultural managers seeking to involve younger generations in heritage preservation.