Higher Wages for American Workers Act of 2023 This bill increases the federal minimum wage, permanently establishes the E-Verify system and requires its use, and contains other related provisions. Specifically, the bill increases the minimum wage to $11 per hour, phased in over five years (six years for businesses with fewer than 20 employees), from the current rate of $7.25 per hour. The bill also phases in over three years an increase of the minimum wage for new employees younger than 20 years old from $4.25 to $6 per hour, and increases the length of time an employee may be paid this lower minimum wage. Both minimum wages shall be adjusted according to the rate of inflation every two years thereafter. The bill also requires employers to use E-Verify to electronically verify the employment eligibility of new employees, with phased-in deadlines that generally require all employers to comply within 18 months of this bill's enactment. This bill provides for various requirements related to E-Verify, including requiring employers to examine and verify certain identifying documents belonging to the employee. The bill increases civil penalties for various violations related to hiring, recruiting, and referring ineligible individuals. Repeated violators may be debarred from receiving federal contracts, grants, or cooperative agreements. The bill also increases criminal fines for violators that engage in a pattern or practice of violations.