1) Try adding a request for attachments within the e-sign platform itself. They can upload directly into the DocuSign.
2) Make sure you're using some email platform with "templates" so that you can send the request out quicker with a link to the app, rather than logging into the eSign platform each time and sending out a personalized request
3) Integrate Zapier to the above

Most platforms that are not Docusign are cheaper BTW, lemme make an intro.