Azure AD - SAML with 3rd party as IDP

Question

My current setup is .net web application plus Azure AD as IDP for my application. My application is a public web application where anyone can sign up and get in. We are in process of signing up a contract with one of our clients who already have their website and IDP (non-Microsoft).

Our requirement is that users login to their website, lets call it www.client.com and my website as www.mysite.com. So user "A" logs into www.client.com. User "A" sees a button "Go to mysite.com" on www.client.com. Once "A" click on this button, if he exists on mysite.com, he sees dashboard directly but if "A" does not exist - he sees mysite.com signup page.

Question: Is it possible to have SAML based trust relationship between their non-microsoft IDP and my Azure AD which acts as service provider? if yes, how is it implemented so users dont see login page and auto-login to mysite.com if exists.

So users from client.com should not see login page on mysite.com. If they are logged into client.com, they should be auto-logged into mysite.com.