Rollouts of COVID-19 vaccines in the USA were opportunities to redress disparities that surfaced during the pandemic. Initial eligibility criteria, however, neglected geographic, racial/ethnic, and socioeconomic considerations. Marginalized populations may have faced barriers to then-scarce vaccines, reinforcing disparities. Inequalities may have subsided as eligibility expanded. Using spatial modeling, we investigate how strongly local vaccination levels were associated with socioeconomic and racial/ethnic composition as authorities first extended vaccine eligibility to all adults. We harmonize administrative, demographic, and geospatial data across postal codes in eight large US cities over 3 weeks in Spring 2021. We find that, although vaccines were free regardless of health insurance coverage, local vaccination levels in March and April were negatively associated with poverty, enrollment in means-tested public health insurance (e.g., Medicaid), and the uninsured population. By April, vaccination levels in Black and Hispanic communities were only beginning to reach those of Asian and White communities in March. Increases in vaccination were smaller in socioeconomically disadvantaged Black and Hispanic communities than in more affluent, Asian, and White communities. Our findings suggest vaccine rollouts contributed to cumulative disadvantage. Populations that were left most vulnerable to COVID-19 benefited least from early expansions in vaccine availability in large US cities.