Medication Access and Training Expansion Act of 2020 or the MATE Act of 2020 This bill requires prescribers of controlled substances, as a condition of obtaining or renewing their registration with the Drug Enforcement Administration, to complete specified education or training on the prevention, treatment, and management of opioid-use and other substance-use disorders. This education and training shall also satisfy the training requirements currently needed to obtain waivers to prescribe certain medication-assisted treatments for opioid-use disorders in settings other than opioid treatment programs.