SSO with other domain

I have a web app that is using Auth0 for authentication.

App owner partnered with another org and they would like to provide seamless login experience to other website users.

It should work like this:

  • If user comes from other website we must log them in automatically without asking login and password
  • If that user is not registered with us, we must automatically create new user without asking them anything
  • In all cases user experience is they login on other website, click on a link to ours and they already logged in on our website

Other website is using YourMembership platform to manage users. And we are using their API to get info about current user.
Than we can find that user by email in Auth0.
But how can we actually log them in programmatically? Without asking credentials.

Or maybe the approach is wrong overall.
Would appreciate suggestions