In order to setup your account to trigger document generation for guest users, you have to use custom Apex and Triggers to execute the required methods instead of utilizing Record Trigger Flows. This means triggering document merges without the use of mapping.
For a walkthrough of how to setup Formstack Documents to trigger document generation as part of Apex code, check out this article as well as a preview of what the Apex code would look like below.
To send data over to Formstack Documents to merge into a document (without a mapping), you can use this function to return the HttpResponse from the merge request to save the file/response from there:
HttpResponse doMerge( MapmergeData, String mergeUrl );
or
HttpResponse doMerge(
String jsonString,
String mergeUrl
);
In addition to setting up the code, you would need to apply the user permissions specified in this article.