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Promoting educational upward mobility among first-generation college students (FGCS) represents a common global challenge in advancing educational equity. Utilizing data from the China College Student Survey, covering 457,282 students from 99 higher education institutions, this study investigates the determinants of FGCS' aspirations for postgraduate education.Employing logistic regression analysis and Shapley value decomposition, the findings reveal that institutional support plays a substantially more critical role in shaping FGCS' aspirations. Moreover, the impact of institutional support intensifies as students progress into their junior and senior years. The study highlights the necessity for targeted institutional support and comprehensive dissemination of educational opportunities and benefits to elevate FGCS' postgraduate aspirations, thereby advancing broader educational equity.