Universal Child Care and Early Learning Act This bill provides funds to the Department of Health and Human Services (HHS) for an affordable child care and early learning program. Children who are at least six weeks of age but not yet required to attend school may participate in the program regardless of family income, disability status, citizenship status, or employment of a family member. Under the program, HHS must support sponsors (e.g., states, local governments, tribal organizations, and nonprofit community organizations) that provide child care and early learning services for families. Families must pay a subsidized fee, based on their income, for the services. The fees are waived for children from families with incomes below 200% of the poverty line. The fees are capped at 7% of a family's income regardless of the family's income level.