Significance Species with narrow distributions provide unique opportunities for understanding the mechanisms that limit their spread. We studied a marine invader that exhibits ecological dominance within its range and has the capacity to fundamentally alter the coastal habitat when introduced to new locations. We found evidence of the species’ potential to establish itself far beyond its present introduced range from both genomic data and species distribution modeling. Therefore, minor oceanographic changes (due to, for example, contemporary climate change) or alteration to human-mediated dispersal may trigger a large-scale invasion along vast stretches of coastlines. Our work provides a holistic framework to assess potential changes in the distribution of invasive species.