Undertaking National Initiatives to Tackle Epidemic Act of 2020 or the UNITE Act of 2020 This bill responds to the COVID-19 (i.e., coronavirus disease 2019) public health emergency by increasing volunteer opportunities within AmeriCorps and employment opportunities at the Federal Emergency Management Agency (FEMA), and requiring the re-enrollment of Peace Corps volunteers whose service ended involuntarily on March 15, 2020, or earlier for volunteers who were serving in China and Mongolia. Among other things, the bill reauthorizes through FY2022 AmeriCorps programs; increases recruitment levels of its volunteers to 500,000 in FY2020-FY2022; sets the minimum compensation for AmeriCorps volunteers, beginning in FY2020, at 200% of the poverty line applicable to a family of one; increases the ceiling on grant amounts to such volunteers from $18,000 to $25,000 and the grant maximum amount limit to meet program needs; requires FEMA to appoint, administer, and expedite the training of an additional 62,000 Cadre of On-Call Response/Recovery Employees in FY2020-FY2022 above the level of such employees in FY2019 to address the COVID-19 health emergency; and authorizes the President to pay a state, tribal, or local government in which a major disaster has been declared stipends for temporary workers conducting nonpartisan official election poll worker services.