1. University, some time after it. No much obligations. Take low-effort job to sustain yourself (maybe freelance), spend the rest of the time contributing to open source. Treat it as a time to learn. The main goal is to become good. You can learn very different things by contributing to OSS packages, as compared to working for some outdated local company. Try to internalize how popular software is organized, how people review code, etc. Find people you respect, work with them. You don't need to have a shiny CV and pass technical interviews to work with great people you can learn from, developing great real-world technology, solving hard problems.
2. You need a real job. Try to find one which allows you to spend some time doing Open Source; have it as an important criteria for choosing a job, among salary, work environment, etc.
For me two types of companies worked as a "real job" which allows OSS contributions.
First, some small startups / companies. They often don't mind if you open source a few libraries from the codebase you've created, because usually it is not the code itself which is important for startups; they're trying to find product-market fit. For them a benefit is that code become organized better (after an idea fails, code can be reused for the next idea), and developers are happier, so it can be win-win. You won't be working on open source full time, but you'll be able to create something useful, and spend significant amount of time on it.
Second, there are companies which are built around open source, or contributing a lot to open source. Often there is a company behind a popular OSS software (e.g. Elasticsearch for Elasticsearch, or Scrapinghub for Scrapy). Sometimes company's github has many actively developing OSS projects, which is a good sign. Look for such companies, apply. There is a higher chance to be able to work on open source if you join such company. It is not given you'll be allocated to work on OSS, but a previous experience maintaining Open Source and contributing to it helps. That's good to be proactive here - use your experience gained from unpaid OSS work or small startup OSS work, start contributing without being asked.
According to my experience, working full time, having family and having significant Open Source contributions is very hard, unless an employer supports it, or unless the job is not really a full time job.
There are "rockstars" which are able to sustain themselves just by working on their own OSS projects, but I think currently they are outliers, not a norm. It may be possible to do this, but I've personally seen way more opportunities to do sustainable OSS work as a part of day job, as compared to donations or a new business.