Check if logged in with IDP?

I have an odd case where an application needs to check whether or not the user is already logged in with the IDP. If they are not, then the application would not initiate authentication. If they are logged in with the IDP, then it would authenticate. What I don’t want to happen is for the user to get the login screen from the IDP in either scenario. I’m sure this is probably not possible, but figured it wouldn’t hurt to ask.

I’m afraid that checking with the IdP whether the user is logged in is not supported by the SAML specification.
You would need some proprietary way to perform this check.