How do I share an Auth0 session across apps

This has probably been addressed, but I couldn’t find it in the community.

My scenario is that we are using GSuite as an IdP. We use that connection across multiple apps. The first app is a third party tool which uses SAML 2 for authentication. The second app is a home grown application that uses Auth0 for authentication.

What I am trying to accomplish is having a user authenticate (through Auth0 based on domain configuration which could be SAML, username/password, etc.) into the home grown app, then be able to click a link directly into the third party app without authentication again.

Currently, Auth0 handles the initial authentication well, but forces a second authentication when heading to the third party app.

We are linking to the third party app using the Auth0 IdP init link that looks like https://{domain}{app_identifier}. As I understand, this should validate the Auth0 session (that was established during authentication to the home grown app) and issue a SAML token with a redirect to the third-party app. Instead, I have am forced to authenticate again.

What am I missing?