‘Born sustainable firms’ (BSFs) — firms founded with an explicit strategic intent to operate in a sustainable manner play an important role in the sustainability transition and represent a significant but underutilized research site. Adopting the dynamic capabilities (DC) perspective, this paper explores BSFs' pursuit of their environmental and social goals. Having first assessed and confirmed its relevance to the BSF context, a high level framework of DC processes is operationalized. Through a dialogic approach, comparing the literature and empirical material from 12 BSFs from a wide range of sectors and locations, an in‐depth picture of 28 processes underlying sensing, seizing and transforming meta‐capabilities emerges. All but one of the detailed processes can be linked to prior research and are specific, though not unique, to BSF. Whilst the operationalized framework of DC processes in the BSF context extends prior research, the established notion of competitive advantage — framing organizational goals and impact in terms of financial outcomes and strategic performance relative to rivals — is problematic in this context. We therefore reconceptualize BSF's organizational goals and impact in terms of ‘sustainability advantage’, that is, maximization of environmental and social performance within the constraint of economic viability. In addition, we identify two key dimensions of advantage: time horizon, which ranges from immediate to longer term impact, and scope, which ranges from organization‐centred to system‐wide impact. The findings have clear implications not only for sustainable entrepreneurship but also for incumbent firms moving towards genuine sustainability.