Hello. Thanks for reading and for asking.

To invoke a Google Cloud API, you need to have a Google identity (user account or service account). In your case, if it's a Google Cloud Identity platform or firebase auth identity, it won't work out of the box.

I think you can achieve that by using Workload Identity Federation. Use your current system as an OIDC provider and impersonate a service account to get a valid access/identity token.