We don’t have one API call that does it all, but we do have a call that will return all file paths deployed with your site: https://open-api.netlify.com/#operation/listSiteFiles
So you’d make a GET request to that endpoint, check the
path that’s returned for each file, and then you’d have to write code to download each of them (each file will be available at your-netlify-url.netlify.app/:path-returned-by-api-call
You can use Netlify’s js-client or Postman to make that call. You will need a personal access token, which this article describes how to get:
Let us know how it goes or if you run into any issues along the way.