Veterans' Entry to Apprenticeship Act of 2019 This bill requires the Department of Veterans Affairs to provide the same amount and type of educational assistance to pre-apprenticeship programs as apprenticeship programs in certain circumstances. A pre-apprenticeship program is designed to prepare individuals to enter an apprenticeship program via education and training. Under the bill, a pre-apprenticeship program may be treated like an apprenticeship program for purposes of educational assistance if the program complies with state standards or meets other accepted criteria if state standards do not apply. If an individual is not paid as part of a pre-apprenticeship program, they are eligible for a specified amount of housing assistance.