AJAX is only submitting the form (not creating it), so yes, the static form must/will already exist on the site.
If you are rendering a form in JavaScript there is a method for that too.
In either case, there is no way to append elements to the form (like adding extra images—see Append external data to the form in React)
If wanting to give people the option to add more fields, you could add multiple hidden fields to the form and use a button to unhide them, look at submitting using a serverless function (keeping in mind that they have a 10 second execution limit) or use a third-party service.