I’ve had a couple kids want their own ‘school’ at that age. Depending on the child I buy a couple Kumon preschool workbooks (they have themes like a cutting book to work on scissors skills, mazes, pasting, numbers, etc). Then I gather a few hands on manipulatives or games (dominoes, counting bears, puzzles in varying difficulty levels, a Melissa and Doug wooden clock puzzle, playdoh, etc). Then I grab stacks of picture books and put them in a bin just for us.
Here is the KEY: I never say “Hey 4 year old, it’s time to do school. Come sit down with me.” Never ever. Instead, any time they come to me and say “Can I do school?” I say sure and point them to those bins just for them. They choose an item and we do it together. When they get bored/distracted/done we’re done. I never try to do “one more page, one more book, one more letter”.
I have had some 4 year olds who will ask every single day for weeks and months on end to do their school. I have had some who ask once every few weeks once they have their bins. They just like knowing it is an option and go about their play instead.
Right now I’m on 4 year old #8 of 10. He’s usually playing, but there are a couple activities he regularly asks to do. One is using a chalkboard for writing letters. So when he asks, I say yes. When he doesn’t, I don’t suggest school.