Gateway engineering courses often expose accumulated gaps in students’ foundational knowledge, affecting progression and retention. This study investigates early predictors of completion and performance in Machine Elements, an integrative second-year mechanical engineering course at the University of Zagreb. A retrospective cohort dataset of 2351 students enrolled between 2013 and 2021 was analysed using admission variables, first-year course grades, and exam-attempt indicators. Cohort differences were examined with descriptive statistics and non-parametric tests, while course completion was modelled using logistic regression, LASSO-based predictor selection, and temporal validation. Students who completed the course differed most consistently from non-completers in Strength of Materials performance and prerequisite exam attempts. A reduced five-predictor model retained most of the full model’s predictive ability, achieving ROC AUC = 0.749 in the pooled sample and 0.726 in temporal validation. Intervention-oriented evaluation showed that Top-K risk selection provided high precision but low sensitivity under limited support capacity.