Is it possible to create a brand new google app script programmatically and attach him to a specific google doc?
Or in any other way, to make 1 bound script and make several google docs to share him as the same bound script?
Yes. Possible through the API.
Use project.create. You can provide a project title. You can also create a bound script by providing the Google Drive ID of a Google Doc, Sheet, Form, or Slides file to act as the script's parent.
clasp is an open-source tool, separate from the Apps Script platform, that lets you develop and manage Apps Script projects from your terminal rather than the Apps Script editor.