Expediting the EIDL Program Act of 2020 This bill modifies the disbursement of economic injury disaster loans by the Small Business Administration (SBA) with respect to such loans made in response to COVID-19 (i.e., coronavirus disease 2019). Specifically, the bill authorizes the SBA to increase the amount of a disaster loan to a small business by 20% to cover costs related to continuity of operations and risk mitigation improvements. The bill also authorizes the SBA to make such loans to startups and to waive rules related to affiliation, and it requires the SBA to waive the personal guarantee requirement on such loans made to cooperatives. In addition, an applicant for a disaster loan may request an advance on such loan up to a specified amount, and they shall not be required to repay any amount of an advance if they are subsequently denied a disaster loan. The bill also authorizes the SBA to approve an applicant for a disaster loan that is below a certain amount based solely on the applicant's credit score and to use alternative methods to determine such applicant's ability to repay. Further, the bill establishes a maximum interest rate on a disaster loan based on an applicant's ability to obtain credit elsewhere, and it expands the qualifying events for which a disaster loan may be awarded to include emergencies involving federal primary responsibility.