Recent expansions of child tax, food assistance and health insurance programs have made American families' need for a robust social safety net highly evident, while researchers and policymakers continue to debate the best way to support families via the welfare state. How much do children -- and which children -- benefit from social spending? Using the State-by-State Spending on Kids Dataset, linked to National Vital Statistics System birth data from 1998-2017, we examine how state-level child spending affects infant health across maternal education groups. We find that social spending has benefits for both low birth weight and preterm birth rates, especially among babies born to mothers with less than a high school education. The stronger benefits of social spending among lower-educated families lead to meaningful declines in educational gaps in infant health as social spending increases. Finally, mediation analyses suggest that social spending benefits infant health through mothers' increased access to prenatal services, as well as improvements in health behaviors. Our findings are consistent with the idea that a strong local welfare state benefits child health and increases equality of opportunity, and that spending on non-health programs is equally beneficial for child health as investments in health programs.