If 100 developers of equal skill apply to the same job, each has a 1% chance of being accepted. How do you beat the odds?
One way to skip the line of applicants is to create the job yourself. Talk to someone who owns or manages a business or organization. Ask about how they use technology in their organization and find out about their current limitations and challenges. If you have skills that can help them out, explain how the problem could be approached to implement a good solution. Try something small to get started, and seek to build a long term relationship leading to more services in the future. This is a freelance/consulting path, which requires you to be good at marketing yourself and working with people. However, this can be one of the most fruitful and enjoyable career paths, as you get to work on different projects and can have huge impacts on organizations.
Another way to take a shortcut is to get a referral. If you meet someone who works at a company you like, ask them if they would be willing to talk to you about what it's like there, and to review your qualifications. Seek their advice on how to brush up on any important skills, or how to tailor your resume. If you demonstrate serious interest and show that you're a good fit, they will be happy to recommend you. Many large companies have an internal application system that will bump you into a smaller applicant pool.
Share what you learn by blogging, or posting samples on github or codepen. This goes the extra mile to show that you are passionate about the work and understand the nuance of how to design and build good software. You ask and answer questions on your own, leading to new discoveries, instead of just doing what you're told works. You show that you are highly productive, and care about sharing knowledge with the community. These things are a major asset to any team, and an easy way to stand out.
Get out in the community, go to conferences and meetups. If you can present something, it's a great way to build a reputation and get in contact with people who might need your work. Being part of a professional group is a highly recommended way to meet people who do the work you want to get into. Even if it's a local meetup for the framework you use, knowing other people in the field will expand your opportunities.
Be relentless. It doesn't matter how many nos you hear as long as you get a yes from a good employer you will be happy to work with. Send out as many applications as you can instead of one at a time. If you get a few hits back, you can use them to negotiate a good rate for your work. Some people will have the odds stacked against them for unfair reasons. Do not get discouraged, you will get what you want as long as you don't give up. Do not take things personally, instead try to learn from each encounter and improve yourself so you get a better chance on the next one. The skills you build while making progress against your challenges will become extremely valuable as you advance in your career. Effective communication and conflict resolution skills are essential in leadership and decision making positions, so that the right voices are heard and the best decisions made. Successful organizations choose leaders who can do this effectively instead of letting their own bias cloud their judgment.
The goal of these tips is to hack your luck so you don't need as much. Instead of taking a shot in the dark, we can take a much more tactical approach that will help find more and bigger opportunities. When you've met people in the right places and they know what you can do, you can stop sending out applications and start sorting through requests for help. Remember that you are a specialist, and that there are companies out there that could use your help right now. Just need to connect those dots.
Good luck to those of you seeking a new gig! We have all had different paths, so don't think there is only one way to get there. Just keep trying, keep learning, and especially networking with those who can show you the ropes and point you in the right direction.