The purpose of this study is to determine how introductory Project-Based Learning (PjBL) courses affect the self-efficacy of first-year engineering students. Grounded theory is used to analyze twelve interviews with first-year students about their experiences in two PjBL courses, Engineering Design and Physics Laboratory. Data indicate that students' self-efficacy within each course is correlated with the extent to which their course goal perceptions align with those intended by faculty. In Engineering Design, students' recognition of the faculty's intended course goals corresponds to higher levels of self-efficacy. Conversely, in Physics Laboratory, students' low self-efficacy is correlated with a large gap between their perceived and faculty intended course goals. Analysis further reveals that this difference in course goal perceptions may stem from the variations in the courses' contingent scaffolding. Finally, our findings suggest that students' self-efficacy may be further supported by dynamic course scaffolding that allows for an increase in students' autonomy throughout a course.