If you had backups enabled on your droplet or snapshots of it then it would be possible to roll back to one of those images. If not, and your developer either deleted the files from your droplet or deleted your droplet itself then there is not likely going t be a way to recover them.

One things I will mention. If this was a static website (not interactive) and it was public, it is possible that it may have been cached by google or the Internet Archive. This is not perfect but might allow you to recover some portion of what was lost.