Abstract: As China strives to build a strong nation through education, the quality of postgraduate education serves as a crucial pillar of the national innovation system. The coordinated expansion and connotative development of postgraduate education are essential to its high-quality growth. Survey results reveal that postgraduate students’ core competencies exhibit a distinct U-shaped curve, characterized by an initial decline followed by a sharp rise. The low point in the first year of postgraduate study exerts a negative impact on the overall quality of postgraduate training, and shortening this period is vital for improving educational outcomes. Findings from qualitative research indicate that six factors play significant roles in shaping the shift in postgraduate students’ core competencies from the low point in the first year to the subsequent leap in the second and third years. These factors include personality traits, motivational mechanisms, curriculum design, supervisory relationships, evaluation systems, and organizational culture. Based on an analysis of the causes underlying the initial dip in postgraduate students’ adjustment, this study proposes a comprehensive approach to enhancing students’ core competencies. The proposed strategies include introducing bridging courses to ease the transition from undergraduate to graduate study, reconstructing the curriculum to close knowledge gaps, optimizing the advisor—advisee relationship to balance autonomy and guidance, refining the evaluation system to integrate explicit standards, and fostering a supportive organizational culture. Together, these measures form a comprehensive cultivation pathway to promote the holistic development of postgraduate students’ core competencies.