Background: Mental health challenges have emerged worldwide during the COVID-19 pandemic. University students experienced changes in their lifestyles, academic life, family relationships, earning capacity, and support systems. This study explores the common mental health challenges in university students and their coping strategies using social support in the first wave of lockdowns in Dhaka city in 2020. By learning from young people’s impacts and coping responses, we can help build an improved strategy for future events of this magnitude. Methods: A qualitative study design was employed to conduct 20 in-depth interviews and two focus group discussions with students from purposively selected three public and three private universities in Dhaka city and five key informant interviews with different stakeholders. We used inductive reflexive thematic analysis and applied six phases of the thematic analysis. Codes retrieved from two differently prepared codebooks were merged and compared to identify themes for a fair interpretation of the underlying data. Data were manually indexed, summarized, and interpreted to categorize codes into sub-themes leading to themes. Results: Financial constraints, academic pressure, learning resources shortages, losing confidence, relationship breakup, excessive internet dependency, and traumatic experiences challenged the mental health conditions of the students unevenly across universities during the COVID-19 pandemic. Expressed mental health well-being impacts ranged from anxiety, stress, and depression to self-harm and suicidal ideation. Family bonding and social networking appeared as robust social support mechanisms to allow students to cope with anxiety, stress, and depression. Partial financial subsidies, soft loans to purchase electronic resources, faculty members’ counseling, and sessional health counseling contributed to minimizing the mental health impacts of COVID-19. Conclusion: Mental health is still not a resourced area of health and well-being in Bangladesh. Concentration on developing strong social support and improving increased financial subsidies, including learning resources, can be effective in assisting students in coping with the common mental health burdens during pandemic periods. A national intervention plan should be immediately designed and implemented by engaging different stakeholders including healthcare professionals and establishing effective mental healthcare support centers at universities to avoid immediate and prolonged negative mental health impacts.