The sociology of imagined futures is a growing field of research with a need for empirical as well as theoretical exploration. Theoretically, our article is situated in interpretive sociology and sociology of time, theorising on how future orientation may shape actions and agency in the present. Our analysis is grounded in cognitive dimensions of projectivity to identify variations in imagined educational trajectories. Empirically, we build on a qualitative interview study with newly arrived migrant students between 16 and 19 years old. Two primary trajectories are discerned: untroubled trajectory, characterised by long-term planning, expanding opportunities, and active agency; and uncertain trajectory, marked by a short-term focus, lack of knowledge about the educational system, and a passive stance toward the future. These primary trajectories are further divided into three subtrajectories with distinct properties. The analysis extends the theoretical framework by proposing 'plausibility' as an additional cognitive dimension of projectivity. The study demonstrates how projected future trajectories shape students' present actions, revealing that untroubled trajectories are linked to opportunities, while uncertain trajectories are associated with disadvantages, thereby refining previous research on NAMS's educational experiences and interpretations of their educational prospects.