Just applying to quality job listings and getting responses back is largely the domain of people with some prestige on their resume. A university or name brand employer.
Absent that, your network is the thing. Software developers willing to submit you as a candidate internally or to otherwise vouch for your skills. These can be friends, people you work on hobby or open source projects with, people who read a blog or something you write. The most common source will generally be ex coworkers. If you're genuinely performing above expectations, and you're good to work with, then they should be happy to mention your name for openings at whatever better employers they've moved on to or when they hear people within their own network talking about looking for someone who is good at [your skillset].
"Networking" as an intentional activity is making sure you have the kind of relationships with as many coworkers as possible that when they leave, it wont be weird to stay in touch and talk about what you're both up to every now and then. Increasing the amount of people you have out in the world who know what your current skill set is like and who have spoken to you recently enough that you will pop in to mind when they hear someone looking for it.
LinkedIn is both this on easy mode as well as a way for third parties (recruiters) to see that vouching rather than just your ex coworkers network.
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Then separately from that and not something that would have landed you a 6 figure salary in your current role but that is still crucial. Did you negotiate? Coming from a poor background myself there was a very strong "keep your head down, work hard, and people will just give you more money than they need to" sort of mindset around. If you didn't negotiate, that "just over $20/hr" could very likely have been $30/hr if you had. And whatever your first six figure position is, the offer is likely to start around $80k.
Read this and part two to see the impact negotiating can have for your income: https://haseebq.com/farewell-app-academy-hello-airbnb-part-i...
Then this from HN regular Patio11: https://www.kalzumeus.com/2012/01/23/salary-negotiation/