How to authorize sigstore with gcloud auth access-token?

I’m trying authorize sigstore (software artifact/s signing tool),
default workflow:
it follows a WebAuthFlow i.e redirects to a browser to authorize oauth2.sigstore.dev to sign the artifact, to provide itself with an oidc token consists
iss: “https://accounts.google.com
aud: “sigstore” and rest as usual
here’s the AuthorizationCodeFlow of how currently sigstore WebOidcClient does it
sigstore-java/sigstore-java/src/main/java/dev/sigstore/oidc/client/WebOidcClient.java at main · sigstore/sigstore-java · GitHub
I’m trying to do similar by using gcloud auth access-token instead of the usual WebAuthFlow, how can i do that?