Child Care for Working Families Act This bill provides funds and otherwise revises certain child care and early learning programs for low- to moderate-income families. Specifically, the bill provides funds for the Child Care and Development Block Grant program and reestablishes it as a child care and development assistance program. The bill also allocates program funds for states to provide services and supports to infants, toddlers, and children with disabilities. Further, the bill revises the program to require each state to create a tiered and transparent system for measuring the quality of child care providers, which must include evidence-based standards and payment rates that are based on a certain cost estimation model; ensure that copayments are based on a sliding scale and that no family receiving assistance pays more than 7% of its household income on child care; and use quality child care amounts for certain activities, such as increasing the supply of child care providers. The bill also provides funds and establishes grants for states to create preschool programs for low- to moderate-income children between the ages of three and five years. The Department of Health and Human Services (HHS) must make grants to Head Start agencies to provide children with access to full-school-year and full-school-day services, provide access to additional service hours for migrant and seasonal agencies, or enhance the quality of existing services. Finally, the bill requires, and provides funds for, HHS to assist Head Start agencies with ensuring their teachers and staff are paid a living wage.