Ask HN: Built a site with established competitors for SEO. What to do?

Hello, I built a sudoku webapp with SEO being the last thing I considered. This is because I wanted to learn how to build apps and also have assurance there was demand for it.

Months after completion the site still has few visitors (~20 per day, mostly from one referral link I managed to get). It's hopelessly invisible from Google due to established sudoku sites and that it has few keywords due to being an app.

I created a widget for others to add puzzles to their sites with only a few takers.

Posting the link around the internet brings some visitors but nothing sticks.

What would you do in this situation to get this site on the first page of Google? Or do I have a hopeless chicken and egg scenario?

I believe my site is at least a good as the others - it's just that without Google traffic I can't reach critical mass. Sharing via FB and Twitter just doesn't happen often enough.

Thanks.