This paper studies the interaction between the decrease in the gender pay gap and the stagnation in the careers of younger workers, analyzing data from the United States, Italy, Canada, and the United Kingdom. Our findings highlight the importance of labor-market entry to understand the shrinking of the gender pay gap. The entire decline in the aggregate pay gap originates from (i) newer worker cohorts who enter the labor market with smaller-than-average gender pay gaps and (ii) older worker cohorts who exit with higher-than-average gender pay gaps. Convergence at labor-market entry originates primarily from younger men's positional losses in firms' hierarchies and the overall pay distribution. We propose an explanation by which a larger supply of older workers can crowd out younger workers from a limited number of top-paying positions. These negative career spillovers disproportionately affect the career trajectories of younger men because they were more likely than younger women to hold higher-paying jobs at baseline. Consistent with this aging-driven crowd-out interpretation, younger men experience the largest positional losses within the hierarchies of firms that are more exposed to workforce aging. These findings hold after controlling for alternative explanations for the progressive closure of the gender pay gap at labor-market entry. Finally, we document that labor-market exit has been the sole contributor to the decline in the gender pay gap after the mid-1990s, indicating that without structural breaks, the closure of the gender pay gap is unlikely in the foreseeable future.