Use terraform to run a scheduler with firebase

Terraform Providers Google
1

I am trying to run a scheduler (firebase function)

export const notificationScheduler = onSchedule('*/5 * *  * *', async() => {
  sendNotification();

But I wonder how I can use terraform to deploy the scheduler. So far, my attempt is to rewrite this function as an express application and use

resource "google_cloud_scheduler_job" "job" {
  name             = var.scheduler_name
  project          = var.project
  region           = var.region
  schedule         = var.schedule
  time_zone        = "Europe/Paris"
  attempt_deadline = "320s"

  http_target {
    http_method = "GET"
    uri         = "${google_cloudfunctions_function.function.https_trigger_url}/scheduler/update-episode"

    oidc_token {
      service_account_email = google_service_account.service_account.email
    }
  }
}

But I wonder if there is not a way to deploy the scheduler directly without having to rewrite it as a request to an express server