Not writing an answer but rather linking the official Cognito doc, that talks about Setting up SAML Federation in AWS Cognito for IDP initiated Single Sign On (SSO).

https://aws.amazon.com/blogs/security/how-to-set-up-saml-federation-in-amazon-cognito-using-idp-initiated-single-sign-on-request-signing-and-encrypted-assertions/

Hope this helps you as much as it helped me.