Whilst not ideal, another Alternative might be to utilize the custom authentication feature available with identity platform https://cloud.google.com/identity-platform/docs/web/custom”,

For this you would need to implement your own OAuth2/OIDC flow to this non-standard provider outside of firebase/identity platform, there are many frameworks to facilitate this, and then once successfully authenticated, create a JWT (as instructed in the link) and sign in to firebase/identity platform.

Presuming you require it, this method would allow you to continue to use the services/ alternative providers offered by firebase auth and centrally manage your users.

Note, careful consideration should be made regarding token refresh and revocation of users authenticated in this way.