Federal Implementation of Recruiting, Staffing, and Triage for COVID-19 Care Delivery Act of 2020 or the FIRST COVID-19 Care Delivery Act of 2020 This bill contains provisions to increase the number of health care professionals during an emergency period, in particular the COVID-19 (i.e., coronavirus disease 2019) emergency, such as by relaxing certain immigration requirements. The Department of Homeland Security (DHS) shall provide lawful permanent resident status to a qualifying alien who served as a physician or nurse during the COVID-19 emergency and is not otherwise ineligible for such status. To qualify, the alien must have (1) received an H (specialty profession) or J (exchange visitor) visa, (2) received temporary protected status, or (3) been covered under the Deferred Action for Childhood Arrivals Program. For an alien seeking lawful permanent resident status under this bill, DHS shall waive (1) certain eligibility requirements, such as any applicable foreign residency requirements; and (2) any annual numerical limitations. During an emergency period, DHS shall waive (1) any annual numerical limitations for a qualified alien seeking admission under an H or J visa as a physician or nurse, and (2) the two-year foreign residency requirement for certain aliens seeking readmission as a physician or nurse. During an emergency period, the Centers for Medicare & Medicaid Services (CMS) shall not impose any caps on the number of medical interns enrolled in any CMS-funded programs. In such a period, a state may waive licensing requirements for an alien physician or nurse admitted under an H or J visa.