1. ML/DL Researcher
2. Data scientist - 20/80 engineering vs modelling
3. ML Eng - 50/50 (or 70/30) engineering vs modelling
People suggesting working in engineering to support ML are right that there's a lot of demand, but it's not what you're asking for.
Becoming an ML/DL researcher working on novel techniques or new models will be hard without academic research experience. Few companies are big enough to support true research, and the ones that are have a very high bar even for people with PHDs
What I call "data scientists" apply math/ML to real problems. The people I see here have a quantitative background like physics/math/CS. Often they have more general quantitative skills that go beyond ML. People like this will might work on things like fraud where an eng pipeline exists and small improvements in the model are valuable.
There are more of these roles than "true research" and they exist at small companies because it's applied. You can get into this with demonstrated evidence in side projects + a convincing background, but professional education might be the most sure way.
Finally - there's a lot of demand for engineers who can do both modeling and the requisite engineering. A model is a small part of what goes into a production ML feature - you need a data pipeline, automated retraining/prediction, a place to deploy the model, monitoring on eng stats + data stats, and the usual application backend/frontend to do something with the results.
You might be able to get into this with some demonstrated experience in side projects assuming you're a SWE already, and depending on your standards for where you want to work.