(Question) Using a .EDU to rank a website.

I am the web master for a major universities website and was trying to think of some ways to leverage their authority for one of my sites. Of course I want to be under the radar as much as possible so I was thinking maybe a page with some relevant keywords and links or maybe uploading a pdf to one of the pages. Any thoughts?

Hi there. Not sure if a EDU website will rank better. It would be too easy to just purchase an domain right? Usually for SEO... the Site Age matters, so the older the better in order of organic traffic. Also backlink of course are important since this is to be seen as social proof kinda signals. But i would also be interested if there is maybe some evidence that edu might rank better.