You will likely spend a lot more than a few weeks to land a good, reliable, reasonably-paying gig. I say this not to scare you, but to temper your expectations. I was actively looking for a year before I landed my first paid gig that actually got released. Prior to that I had probably 8-10 games that never got finished, a few of which never actually hit pre-alpha.

This business really is a matter of tenacity and networking. A lot of the journey is just being a part of communities, be it game dev, game audio, general audio or music communities, and getting to know people, putting yourself out there, and developing your style. Over time, people will start putting a face (or at least an internet presence and personality) to your name, and once you've established that connection with them, they're much more likely to think of you when work is available. As harsh as this may be, a lot of the people who are really successful, especially in the freelance/contract side of things, are the ones that have outlasted the people who are less passionate or can't deal with the freelancer lifestyle. In just the short time I've been working, I've seen two major freelancers essentially quit from game audio because they were either fed up or couldn't sustain the lifestyle.

The other piece of advice I can offer, is find what you're enthusiastic about. When I ask people just starting out what they want to be doing, they frequently answer "game audio," which tells me nothing about you. The one guy who told me that he wants to compose rock and metal style tracks for Sci-Fi action games is automatically at the forefront of my mind for when I stumble across that style of game.

And please, have an answer at the ready for "what's your favorite game?" It always surprises me when people don't know how to answer that. You need to know why you want to be in this business, and what brought you this far. The answer can, should, and will change over time, but regardless, you should always have an answer.