Students who are the first in their family to go to university (first-generation students [FGS]) are still underrepresented at universities. One of the considered reasons for this is their lack of social support. Our study followed a group of German students at two time points: after their first educational choice and at the end of their first semester. According to social cognitive career theory, we tested for the effect of self-efficacy beliefs on intention to drop out, mediated by confidence in vocational choice. Following a social network perspective, we analyzed the moderating effect of support network size and support network quality. The findings reveal a complete mediation and add to the empirical evidence on social cognitive career theory. They demonstrate the special importance of social support for FGS. High-quality support networks help FGS struggling with confidence in their vocational choice to follow their university goals instead of dropping out but have no effect for other students.