In this article, we reflect on the functions of outreach in developing the modern scientific mind, and discuss its essential importance in the modern society of rapid technological development. We embed our approach to outreach in culturo-scientific thinking. This is constituted by embracing disciplinary thinking (in particular creativity) whilst appreciating the epistemology of science as an evolving dialogue of ideas, with numerous alternative perspectives and uncertain futures to be managed. Structuring scientific knowledge as an assemblage of interacting and evolving discipline-cultures, we conceive of a culturo-scientific storytelling to bring about positive transformations for the public in these thinking skills and ground our approach in quantum science and technologies (QST). This field has the potential to generate significant changes for the life of every citizen, and so a skills-oriented approach to its education, both formal and non-formal, is essential. Finally, we present examples of such storytelling in the case of QST, the classification and evaluation of which correspond to future work in which this narrative approach is studied in action.