No, Amazon Cognito is not supported by SAML SSO for Atlassian Server and Data Center.

Amazon Cognito can federate with SAML IdPs, but it doesn't act as a SAML identity provider itself.
It can talk to a SAML IdP to do identity federation, but it can't speak SAML to an application like our SAML SSO app.

Since our app is built based on the SAML standard and Amazon Cognito does not support it to talk to service providers, it is not supported by our SAML app to represent your Server or Data Center application as a SAML Service Provider.

Please find more detailed information here:
As you can see in the last step, it will answer with an OIDC token but not with a SAML message.