Depends on what "major contracts" are for you. I can tell you that we don't have any "major contract". We to have several "very nice" ones.
The main way clients came to us is through our website, Dribbble, Behance but also through referrals - people that worked with us in the past, and that recommend our work to a friend. This latter is the oldest but definitely the best marketing you can get!
I am 25. Two years and one month ago I created a company called Pixelmatters (http://pixelmatters.com).
I basically did everything more or less the way you described. Which is something absolutely hard to do. As a result, in Aug 2014 we were 2 but today, as I write this, we are 14 and growing.
Company is profitable, has no VC money and is fully self-funded (initially, by my computer and...a decent internet connection).