Veterans' Entry to Apprenticeship Act This bill requires the Department of Veterans Affairs to treat a pre-apprenticeship program as a program of apprenticeship, for purposes of providing educational assistance: (1) if such pre-apprenticeship program is recognized under or compliant with relevant state standards for a postsecondary pre-apprenticeship program, or (2) in the case of a program for which a state does not require any such standards, if the curriculum of the pre-apprenticeship program is approved by a sponsor who certifies that the program will prepare an individual with skills and competencies needed to enroll in a registered apprenticeship program and the pre-apprenticeship program maintains conduct and attendance policies in accordance with such sponsor. A covered individual enrolled in a pre-apprenticeship program must receive the same amount and kind of educational assistance the individual would receive if the individual were enrolled in a program of apprenticeship, with an exception of specified housing assistance if the individual is not paid as part of such pre-apprenticeship program.