Supporting Children's Mental Health Care Access Act of 2022 This bill reauthorizes through FY2027 two grant programs that support pediatric mental and behavioral health services and interventions. First, it reauthorizes and makes changes to a grant program for states, localities, and Indian tribes for statewide or regional telehealth access programs to promote the integration of behavioral health in pediatric primary care. Specific changes include allowing a nonprofit organization to receive the grant if the state (1) does not apply for the grant, and (2) supports the nonprofit's receipt of it. Additionally, recipients may use grant funds to support schools and emergency departments. Second, the bill reauthorizes a grant program for human services agencies and nonprofits to develop and maintain infant and early childhood mental health promotion, intervention, and treatment programs.