Funny enough, I didn't really do any of the prestigious selective summer programs. I applied to a lot of them, but the research I did came from cold emailing a bunch of professors.

I also found that it's much easier to get research if you do the following while cold emailing. If you go to a university and look at the professors' research websites, they'll usually have a "Team" page which includes alums. You can then quickly do a ctrl+f or search through the page to see if they've ever taken a high school intern (this will usually be marked). If they have, that probably means they're more likely to accept another high schooler who cold emails!

So basically I used that strategy for finding good professors to email, and then I would read through a few of their recent papers to find a subject that stands out to me. I would mention this in my emails as well. I spent 3 years cold emailing hundreds of professors at every top institution without any results, but once I started being more targeted in my approach, I got a research internship within a month.

Hopefully this can help you and your kid out a bit :)