Early Childhood Mental Health Support Act of 2020 This bill requires the Department of Health and Human Services (HHS) to identify and review evidence-based interventions, best practices, curricula, and staff trainings in Head Start programs that improve the behavioral health of children and support staff wellness. HHS must (1) award grants to participating Head Start agencies to implement such interventions, and (2) evaluate the implementation of such interventions. The bill also permits HHS to fund five best practice centers in universities to prepare future Head Start agencies and staff to deliver such interventions.