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The escalating incidence of depression has brought attention to the increasing concern regarding the mental well-being of university students in the current academic environment. Given the increasing mental health challenges faced by students, there is a critical need for efficient, scalable, and accurate screening methods. This study aims to address the issue by using the General Health Questionnaire-12 (GHQ-12), a well recognized tool for evaluating psychological discomfort, in combination with machine learning (ML) techniques. Firstly, for effective screening of depression, a comprehensive questionnaire has been created with the help of an expert psychiatrist. The questionnaire includes the GHQ-12, socio-demographic, and job and career-related inquiries. A total of 804 responses has been collected from various public and private universities across Bangladesh. The data has been then analyzed and preprocessed. It has been found that around 60% of the study population are suffering from depression. Lastly, 16 different ML models, including both traditional algorithms and ensemble methods has been applied to examine the data to identify trends and predictors of depression in this demographic. The models' performance has been rigorously evaluated in order to ascertain their effectiveness in precisely identifying individuals who are at risk. Among the ML models, Extremely Randomized Tree (ET) has achieved the highest accuracy of 90.26%, showcasing its classification effectiveness. A thorough investigation of the performance of the models compared, therefore clarifying their possible relevance in the early detection of depression among university students, has been presented in this paper. The findings shed light on the complex interplay among socio-demographic variables, stressors associated with one's profession, and mental well-being, which offer an original viewpoint on utilizing ML in psychological research.