Automatic link to latest media (zip) file

I’m building a press site theme for use on a multisite installation which has the very specific need of linking to a zip file. I can’t override the upload location of the media library so I need to automatically link to the latest zip file so that nobody has to edit the theme manually to change the link.

Has anyone got any clues on how to achieve this?

*edit* Not absolute beginner at theme building so hopefully you won’t be able to scare me too much with your big boy talk.