Effective climate change mitigation necessitates swift societal transformations. Social tipping processes, where small triggers initiate qualitative systemic shifts, are potential key mechanisms instigating societal change. With large shares of the world's population coastally concentrated, sea-level rise is among the most severe impacts of climate change. Here we combine future sea-level rise estimates, social survey data, and a social activation model to exemplify a transformative pathway where climate change concern increases the social tipping potential, and extended anticipation time horizons shift the system towards an alternative sustainable state of climate action. We find that in many countries, climate change concern is sufficient, such that opportunities for social activation towards this tipped state already exist. Further, drawing upon the interrelation between climate change concern and anticipation of SLR, we find evidence of three qualitative classes of tipping potential that are regionally clustered, with greatest potential for tipping in Western Pacific rim and East Asian countries. These findings propose a transformative pathway, where increased climate change concern shifts tipping potential upwards and extended anticipation time horizons lowers the required size for critical interventions necessary to kick a social system into a more sustainable state.