It is the intent of the Legislature that the department 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, 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 10371, 10372, and 10372.5 cover the cost of this care.