You can do it some day... Only one factor is available from your competitors that is domain age you can't beat it. Any other SEO factors you can beat. Start with On site SEO then move on to well planed link network.
You need to check your competitor everytime if you want to do that at the same time you need to continue writing useful and unique contents to your site/blog.....You can also try promoting it offline
Could you please share with us. What your going to do (seo) for your health website appearing in first position. Eager to hear your reply.