Reforming the professionalization experiences of future faculty members, including their undergraduate experience, provides a possible means to create scalable change in higher education. However, this requires an understanding of where faculty undergraduate training occurs. We analyze data from 7748 tenure-line faculty members across 611 U.S. physics departments, including their undergraduate alma mater and their employer university. The resulting undergraduate professionalization network reveals a prestige hierarchy similar in strength to those previously found in hiring networks at the Ph.D. level, indicating that the road to faculty jobs begins during undergraduate admissions. Furthermore, 42% of physics faculty members earned their undergraduate degrees from institutions outside of the United States. These results reinforce the importance of institutional prestige in academia and offer a potential strategy for driving systemic change.