We wouldn't just fund Head Start. We would send a selection of books to households every year starting from the birth of their kid. My administration would compile a list of broadly acceptable books for babies and small children and let parents choose several per month or year, with a default selection provided if we don't get a form back.
These would be mainly older classics that adults in past generations have already read and that are popular, we wouldn't be springing things on people.
This would be automatic from birth. We're doing Finland style baby boxes. People over like age 15 can select their own books with the library card program which is detailed elsewhere, but we need to ensure that there are reading materials available for babies and learning readers.