(1) Background: University students face increasing mental health challenges, with sociodemographic disparities shaping well-being outcomes and highlighting the need for machine learning approaches to identify distinct psychological profiles. (2) Methods: This cross-sectional study surveyed 4911 Chinese university students (aged 18–25) using the EPOCH Questionnaire, which measures Engagement, Perseverance, Optimism, Connectedness, and Happiness. Data were collected via WenjuanXing (WJX), with recruitment promoted through official channels. Well-being profiles were identified through exploratory K-means clustering, with internal validity and the optimal cluster number assessed using the silhouette coefficient. (3) Results: Cluster analysis identified two distinct groups: Cluster 0 (41.09%) with higher well-being scores and Cluster 1 (58.91%) with lower scores. Differences across all five EPOCH dimensions exceeded 1.0, most notably in Optimism (Δ = 1.31) and Happiness (Δ = 1.37). A subgroup of concern within Cluster 1 (n = 92), primarily male sophomores from rural, low-income, multi-child families receiving financial aid, showed particularly low scores in Connectedness (Δ = −0.57) and Happiness (Δ = −0.43). In contrast, a high well-being subgroup in Cluster 0 (n = 108), mainly urban female freshmen from high-income, only-child families, exhibited elevated scores, especially in Connectedness (Δ = 0.69) and Happiness (Δ = 0.65). (4) Conclusions: This exploratory clustering study identified distinct well-being profiles among Chinese university students, with demographic and socioeconomic vulnerabilities associated with diminished psychological well-being, particularly in Connectedness, Happiness, and Optimism. These findings highlight the need for targeted interventions that integrate psychosocial support with financial assistance to reduce inequalities and promote flourishing.