Early Pell Promise Act This bill authorizes the Department of Education (ED) to carry out an Early Federal Pell Grant Commitment Program under which ED must make a commitment to award Pell Grants to certain students. To be eligible to receive such a commitment, the student must be in grades 8 through 12 and a member of a household receiving assistance under the Supplemental Nutrition Assistance Program. Pursuant to such a commitment, the student shall receive a Pell Grant during the first two academic years of attendance at an institution of higher education (IHE) as an undergraduate if the student files the Free Application for Federal Student Aid form for the award year in which the student will be in attendance at the IHE, and enrolls at the IHE not later than one year after receiving a secondary school diploma or not later than three years after release from the Armed Forces.