Children First Act of 2017 This bill provides additional funding for the Department of Health and Human Services (HHS) to make grants under the Temporary Assistance for Needy Families (TANF) program to provide child care for infants and toddlers under the age of four. Specifically, HHS must make grants to: (1) expand access to high-quality child care for infants and toddlers who do not receive child care funded through the Child Care and Development Fund (CCDF), (2) increase the quality of child care funded through CCDF, and (3) provide financial incentives to highly-qualified child care providers and their workforce. HHS may make grants to enable the provision of child care during nontraditional and unpredictable hours. Under current law, an individual is exempted from TANF's mandatory work requirements if the individual is a single custodial parent caring for a child who is under 6 years of age. This bill expands the exemption to include a single custodial parent or other individual with custody caring for a child who is under 13 years of age.