I think you’ll just need to try for the next session. This is the time of year when many programs fill instantly with divers excited after a season of summer dive team. Try again in the winter and even contact Arlington or Dominion about beginner programs mid-season in case they have kids drop.
Next year is an Olympic year so there will be a big bubble of interested beginning divers. If it turns out your kid is really into it, get them into a club program before that rush in late summer 2024.