Is there a way to only create the "default" hosting site for Firebase hosting?

I have tried using google_firebase_hosting_site to set up hosting in Firebase.
It seems like when using it that it will create both the default site as well as the specified site.
Is there a way to only create the default site?

The site argument seems to be required and I am not allowed to just leave it with the name of my project, since it gives my an "Error creating Site: googleapi: Error 409: Site projects/XXXX/sites/<SOME-NAME> already exists` error

If I do

resource "google_firebase_hosting_site" "full" {
  provider = google-beta
  project  = google_project.default.project_id
  site_id = "${var.project_id}-other"

then it works, but it has now created 2 different sites.