1) You and your child lobby your high school physics teachers to sponsor it. Offer to pay the cost yourself. Make an appointment with school counsellor to advocate for your child.
If it does not work,
2) Look up the semi finalists from last year, and find a winner from your neigboring high schools. They publish the sponsor teachers' name. Contact a sponsor teacher, and beg him/her to let your child to take the contest with their students this year. Offer to pay your child's test cost.
If you look at the semi-finalist of F=ma, It is kind of 拼学校。If your child is in an ordinary school and you still want him to excell in academic competitions, have to be a snowplow parent to convice schools at least to sponsor the contests. Many schools don't actually take students' requests seriously, and at that time parents have to get involved.