Supporting Our First Responders Act This bill establishes a competitive grant program to support medical transport and emergency medical services (EMS). The Department of Health and Human Services (HHS) must award the grants to EMS organizations (including for-profit organizations) or state, tribal, territorial, or local governments. Grant-funded activities include (1) providing salaries and stipends for EMS workers; (2) purchasing vehicles, personal protective equipment, and other resources; and (3) establishing community paramedicine or mobile integrated health care initiatives. HHS must also report to Congress about health insurance reimbursement for medical transport and EMS and the feasibility of establishing a federal EMS office.