Services and Trauma-informed Research of Outcomes in Neighborhoods Grants for Support for Children Act of 2021 or the STRONG Support for Children Act of 2021 This bill establishes two grant programs for governmental health departments to prevent and mitigate childhood trauma and adverse childhood experiences. For the first program, the Department of Health and Human Services (HHS) must award grants to health departments to use data analysis methods to identify interventions to prevent and mitigate childhood trauma. Grant activities include using data analysis to identify geographic areas with a high prevalence of adverse childhood experiences and to implement strategies to improve outcomes for infants, children, and adolescents. For the second program, HHS must award grants to local or tribal governments to establish or expand early childhood trauma-informed care coordination services, including by instituting risk and needs assessments to respond to adverse childhood experiences. For both grants, the bill prohibits the use of funds for certain purposes, such as using the data analysis methods to inform individual case decisions, including child removals, or increasing the presence of law enforcement. In addition, HHS must evaluate and report on these programs and make findings and recommendations publicly available on its website.