Mental wellbeing of university students is a growing concern that has been worsening during the COVID-19 pandemic. Numerous studies have gathered empirical data to explore the mental health impact of the pandemic on university students and investigate factors associated with higher levels of distress. While the online questionnaire survey has been a prevalent means to collect data, regression analysis has been observed a dominating approach to interpret and understand the impact of independent factors on a mental wellbeing state of interest. Drawbacks such as sensitivity to outliers, ineffectiveness in case of multiple predictors highly correlated may limit the use of regression in complex scenarios. These observations motivate the underlying research to propose alternative computational methods to investigate the questionnaire data. Inspired by recent machine learning advances, this research aims to construct a framework through feature permutation importance to empower the application of a variety of machine learning algorithms that originate from different computational frameworks and learning theories, including algorithms that cannot directly provide exact numerical contributions of individual factors. This would enable to explore quantitative impact of predictors in influencing student mental wellbeing from multiple perspectives as a result of using different algorithms, thus complementing the single view due to the dominant use of regression. Applying the proposed approach over an online survey in a UK university, the analysis suggests the past medical record and wellbeing history and the experience of adversity contribute significantly to mental wellbeing states; and the frequent communication with families and friends to keep good relationship as well as regular exercise are generally contributing to improved mental wellbeing.