I believe that being a 'Westerner' definitely works to your advantage for many reasons.
Let me share part of my experience on the subject, as a freelance developer who started in London, then moved on to other 'western' countries. I had no portfolio, having done only bar work since I left Uni, but I was really motivated.
First, as you said, the market is flooded by low-rates developers, asking as little as $3/hour. But the quality of the work they provide, and the heart they put in it reflects the rate they offer. Think about it, if they were skilled enough to ask 10 times the rate they offer, they probably would.
Most of the time, when you put an ad on Elance (now known as Upwork), you receive instantly a dozen of generic replies, often in broken English, and obviously copypasted from a defined set, maybe triggered by a keyword like 'WordPress' or similar. Here's how to take advantage of that:
1. Choose the proposals carefully, and personalize your reply.
Take some time to read the proposal, and start thinking about how you'll solve the client's problem, instead of copypasting a list of your 'skills' that he/she doesn't know anything about. Find something you're interested in doing, and be enthusiastic in your reply. At the beginning, I used to choose only challenging proposals, that I knew I could fix, but didn't know exactly how. I was doing a bit of research on Google, then explained my 'plan' to the client. Often, the actual solution I ended up using was different than the original plan, but it didn't matter, I had made a difference by showing some 'care' in my answer.
2. Emphasize the fact that you do speak English perfectly.
This is a bit controversial, but once the client will have struggled his way through 10 replies full of spelling/grammar mistakes, your proposal will be a breeze of fresh air to him. Remind them of that discreetly in your answer. I usually use almost informal language, to further distance myself from the 'Dear Sir, ...' answers, and I always mention the fact that I do speak good English.
TL;DR: Make your answer pleasant to read, and you'll score more points.
3. Your rate shows your worth, so don't undervalue yourself.
Once again, you want to set yourself aside from the pack. There always will be clients who will choose Price over Quality, but my advice is that you should avoid them, or your hours and stress levels are going to skyrocket, and you'll be back behind your office in no time. If I'm unsure what the client is looking for, I don't give a rate right away, and ask him to clearly to pick 2 out of these 3 things: speed, quality or price (Project Management Triangle). Be daring, and it will pay off, you'll make strong relationships with good people, who will reward you fairly and value your work. That's what I appreciate the most about freelancing, you're not stuck with a nasty boss, ever. That being said, you can set your rate a little bit lower at the start, if you want to build a portfolio quickly. Remember however that you will most likely build long-lasting relationships with your clients, so it'll be harder to up your rate later.
If you do all those things, your portfolio and feedback will quickly match your big mouth (which remains your best asset as it shows confidence), and you'll learn which proposals to answer, and which to avoid. By being 'different' in your approach, you'll become the go-to guy for all your previous clients, and there will be no more competition for you. If you have it in you, it is definitely worth it.