As cultural institutions digitize their archives, they become more accessible and versatile. However, there are significant economic and environmental costs to maintaining large databases over time. Synthetic DNA is an emerging technology that can store data at high density, with almost no energy, for thousands of years. Yet, as technical advances bring DNA storage closer to everyday use, little has been done to understand how we will interact with the technology and accept it into society. We developed an integrated prospective design approach to investigate these challenges. This included participative workshops, narrative building and the design of three tangible DNA storage objects. User evaluations showed how summarized information within the object strengthens understanding and appreciation of the technology. We also gathered insights around material and societal perception. This work opens perspectives for the adoption of long-term sustainable preservation for cultural archives, and pushes prospective design methodologies into far-future contexts.