Use auth0 as saml idp, google as service provider

I am setting up SAML for the first time and i do not have knowledge of SAML.
I am considering the following case:

*Auth0 will be used as the SAML IdP.
*Google Cloud is the ServiceProvider.

I want to create an application with the following flow:

1.Create a new NextJS application.
2.Prepare the login page and homepage in NextJS.
3.When clicking login on the login page, transition to Auth0’s login page, and authenticate with a username and password.
4.After authentication is successful, return to the NextJS homepage.
5.Click a button from the NextJS homepage to open the Google Cloud console screen (assuming it will open without authentication through SAML).

what i have done:

I have create a auth0 tennat and set up a NextJS application following this guide:

I have configured the Google Workspace SAML settings in the same application’s Addons following this guide:

I have configured Third-Party SSO in admin-google-com following this guide:

Currently, I can authenticate with an Auth0 with username and password from my localhost application.
Also, I can redirect to Auth0 and login at console-cloud-google-com using a custom domain user from the browser separately.

My question is:
I want to be able to click a button from a NextJS application and transition to GCP using SSO.
Could you tell me what settings are missing?
Additionally, I would appreciate it if you could provide any sample code or documents for reference.