Adding gravity form to a newly created page programatically

Was hoping someone may have already come up with a solution for this one, but I’m copying an existing template and creating a new form using the gravity forms API. I’d like to then add that to a newly created page, but I’m not seeing a clear way to do that using the wordpress API. Anyone solve this one?

Doesn’t seem to be documented in the wordpress API, but it looks like you can just pass the shortcode for the gravity form as the content in the POST in case anyone else needs this in the future.