My kiddo had to submit a paper for pre-read last year. They submitted it ungraded though later realized that the school probably wanted to see the comments b/c in application they asked for a graded paper. My child also went to a public school but did have a few options for writing samples but agree that there wasn’t a lot and what they had mostly came from elective classes. I think they submitted an essay somewhere in the 3-5 page range. If you really don’t have anything from school that is tough…. You should consider giving feedback to school that they need to assign more writing b/c kids should have had to write a few papers by senior year. That being said, I would share details about lack of writing assigned by school with the coach and get their guidance.