Single sign on works just fine without third-party cookies.
You forward the user to the SSO system with some URL parameters, the SSO system checks the first-party cookies (as the SSO system's domain is shown in the URL bar), then the SSO system forwards the user back to you with some different URL parameters. It can also be done with a popup login window, in many cases.
After all, what if the SSO system needed to ask for the user's password? Your users should know better than to enter their password on a third party's domain - so you need the forwarding mechanism for SSO login anyway.
Single sign on works just fine without third-party cookies.
You forward the user to the SSO system with some URL parameters, the SSO system checks the first-party cookies (as the SSO system's domain is shown in the URL bar), then the SSO system forwards the user back to you with some different URL parameters. It can also be done with a popup login window, in many cases.
After all, what if the SSO system needed to ask for the user's password? Your users should know better than to enter their password on a third party's domain - so you need the forwarding mechanism for SSO login anyway.