It is the intent of the Legislature that the State Department of Education work with Head Start and state preschool programs to generate extended-day and evening care for recipients of aid under Chapter 2 (commencing with Section 11200) of Part 3 of Division 9 of the Welfare and Institutions Code, or any successor program, through recruiting and training parents to be licensed and license-exempt care providers and shall facilitate connections between Head Start and state preschool contractors and child care certificate administrators, including counties and other alternative payment programs, so that funds available for Sections 8351, 8353, and 8354 cover the cost of this care.