You can outrank any authority site if the authority site doesn't have:
- exact keyword in title
- exact keyword in url
- exact keyword in description
- exact keyword in first paragraph
- backlinks with exact keyword
- internal linking with exact keyword
You'll have to apply all the above to your site.
Relevancy beats authority and trust. An authority site can rank on a keyword, even if the page is not relevant, because it has trust. But if a site with no trust at all has relevancy (relevancy means have exact keyword in title, have exact keyword in url, all the above) then it will outrank the authority site.
Relevancy > authority
Authority + relevancy = everything