Experience cloud redirection on login

Hi Community, 

I have an external portal hosted outside Salesforce that our partners (Salesforce portal users) need to access. I’ve set up an Experience Cloud portal and set up SSo with Salesforce as the Identity Provider. The community site is blank, it is only there to handle user creation and password setup. The external site uses REST APIs to fetch Salesforce data for the logged‑in user.

When a new user is created, they receive a “Set Password” link and, after setting their password, are redirected to the community home page which is blank. Is there a way to send them straight to the external portal after they log in? without asking them to enter their credentials again? 

Thanks, 

 Youness