Hi,
in the body of that message there will be a Javascript code that will redirect browser to your IdP. But SAML is available for web services based on SOAP. So I would look there. Especially, have a look at ECP profile.
One of the use cases is: "The client does not support JavaScript, preventing auto form post".
Another option is to use back-channel communication. In this case SP communicates directly with IdP. I assume that in your case you are using front-end communication.
Cheers