Possible or impossible?

Looks like the majority of the competition is getting their authority from other pages as they are already ranking well.

I have this problem in a very specific niche.

I have an entire site that is developed around a theme... maybe 50 pages. While on the first page I can not move up because the sites ahead of me are gigantic brand name sites with mega advertising budgets. They offer little content for the niche... in most cases only a single page.

It's my belief that Google is placing a disproportionate weight on Authority over exact match.

This would also seem to be the case above when you see that the vast number of sites ranking are using neither a Title Tag or a keyword URL.

However the first ranking site kind of proves the point that you can rank by optimizing your site. Clearly they have the keywords, header, and title tag. They are likely targeting this phrase directly.

What I would do is sit on the domain for a few weeks, check back and see if the same site that is number 1 for your search is still number one.

If they are I would look very carefully at what they are doing and emulate it.

Position one is 9 years old but does not have that many backlinks, could be possible.

Its hard to outrank a aged domain name.