The Google Docs API mentions how to get a document with suggestion (track changes), but it says nothing about how to add a suggestion to a document.
How would you insert an edit suggestion in a document using the Google Docs API or Apps Script ?
Unfortunately it isn't currently possible to make suggestions to a Google Doc via the API.
As you've pointed out already, it is currently only possible to view suggested edits but not create them. Aside from the lack of endpoint for them, you can see in the Batch Update and request documentation pages, that there are no entries for suggestions either.
If you really want this to be added to the Docs API (and therefore subsequently in Apps Script) however, you can head over to Google's Issue Tracker and submit a Feature Request asking for this to be implemented.