A site could grow with viral videos on YouTube However, the niche has to be fun so that the videos will be viral. Of course, home business isn't that fun but might go viral.
If you want to go "organic", I don't think there IS a way to get solid ranking without SEO. Oh, sure. You can shoot up to the top doing some "black hat" stuff and maybe stay there for a little while, but you run the risk of getting banned and you can easily get shot down. With quality SEO, I can leave some of my sites alone for months at a time and they're still at the top!
It depends on the kinds of traffic you are getting from different geo graphical location. and the purity and quality of the content which people like to share automatically to other friends and relatives.
Most people seem to be suggesting more SEO just not on page SEO, well potentially all the ways offline businesses promote themselves offline and of course word of mouth. email campaigns if you really have something unique to offer and can get the message across within the subject line, plus use a decent and specific list.
Sites like directories, that are regular updated with dynamic content, don't have to focus so much on SEO
If you are in a niche then good content and very basic seo will do. The search engines will find out good content. Very Broad is a very broad term. If you have something unique or viral in nature then it might work. or have a handsome Marketing budget.
Large amounts of fresh, valuable content, structured correctly and relevant to your theme may "grow" your site into being perceived an "authority site" by the search engines. This should get you quite a lot of long-tail keyword traffic. Other than that, developing some "link bait", eg. some useful software you give away for free, would likely also attract attention.
I keep seeing people state "put good content" "submit unique content" bla, bla... The problem with this is, what does it matter if you stuff your site with unique content if there is little to no traffic to read the content to begin with? Does google like new content, well I am sure they do, but how many can say they put some fresh articles up yesterday, and now I make $1000/mo? I do not object to unique content, but people act as if you put up unique content, then you are in...it is a start, but you are not going to make money over night, unless you just have a super niche that no one else has, then you have google's love, everyone else moves up the ladder the hard way, its a long hard road, and could cost you $1000's of dollars... fresh content or not, it can take a site years to move up the ladder...