When I started on my data science path, about 10 years ago, and there was no training pipeline, so when I dropped out of a PhD a few years later it wasn't that hard to get a data science job with the intersection of skills: math/stats/coding/research. Today that role is probably filled by someone graduating from an undergraduate or grad program, but I know the same company is still hiring for improvements on the research project I helped start.
Good data science, for me, is when you "apply predictive models to end user problems and ship solutions in products", but when I looked around for other jobs I realized that so few companies are able to act cross functionally to exploit the value of ML in products and services. Sure, finance does it, ads does it too, but it seems like the jobs I had access to were some ill-thought out skunkworks that a VP or exec thought was a good idea, or doing work tucked away in some business unit. There are like 10 individual problems there for YC to solve, but the more fundamental issue is that as long as we are still in the hype phase of data science, there will be incentive for business leaders to spend money on it in wasteful ways (at least for your career).
If you want to do data science or ML, it'd encourage you to find tech first companies that are actually using ML to solve real world problems for people, and avoid working on projects that haven't shipped. Also, stay under engineering orgs. In business units, you'll have a boss that doesn't understand what you do, and you'll be promoted out of tech.
Ultimately, I left data science and am now on an infrastructure team at a database company, which is just a better fit for values. If you can get into big tech or any tech first company, the data science is mostly figured out, but in my experience lots of companies aren't offering constructive experience. Good luck.