A better understanding of how to improve student retention in engineering is required to support students in completing engineering degrees and entering the workforce. Application processes to engineering majors are one barrier to retention in some engineering programs. This study evaluates demographic, grades, application process, and engineering major admissions data from students at a large Midwestern University that underwent an application process to engineering majors in Spring 2021 and Spring 2022. Following a common first-year curriculum, students apply to their top three engineering major preferences in their second semester. Applications are reviewed within major departments and students are either admitted to one of their choices, counseled to join a non-engineering major, or must reapply later. Results reveal that first-generation status students are admitted to competitive engineering majors at a significantly lower rate than continuing-generation students. Cumulative grade point average (GPA) is the predominant predictor of major admission and appears to contribute to differences in admission based on students' generation status. A major-specific prerequisite course grade is also a significant predictor of admission into Computer Science and Engineering, although less heavily weighted than GPA. These findings add to our understanding of barriers preventing students from entering engineering and have implications for supporting students equitably through engineering matriculation paths.