I basically did what you’re talking about. Masters in physics, then went into semiconductors as engineer and materials scientist, then switched to Data scientist at a bank for 18 months, and now have been a research scientist in AWS for almost two years.
In Amazon, it’s easy to move around, but not between job families. I think it’s a bad idea to join as a SWE and try to transfer because they want people that have done it before, and you’re unlikely to do that sort of work as an SWE. I think it’s better to get experience in the role you want at a less prestigious company. You’ll learn a ton. Pick the best company that will have you.
My personal turning point was when I did free work for a local startup in exchange for them letting me take the Data Scientist title. To a recruiter, it’s totally obvious to hire a data scientist for a data scientist role, and isn’t clear at all what physics has to do with it. Recruiters are the first step when you’re starting fresh, so make it easy for them.
I also somewhat disagree with many of the comments here that textbooks are better than tutorials. If you buy these 1000 page graduate level texts when the idea that you need to read them cover to cover, you’re likely going to give up and fail. Instead, buy the books and put them on the shelf, and then work through tutorials and examples. Then reference particular sections of the book that are relevant to your work to add depth.
Finally, I recommend against starting with deep learning. There’s a whole helluva lot to learn with basic techniques. Very few companies are actually using deep learning in production systems. Start with linear and tree based methods to learn all the stuff about how to frame the problem and build robust systems. Then you’ll have a deeper appreciation for DL.
A reasonable person could disagree and say that there’s so much domain specific stuff around the art of DL that it really behooves you to start there ASAP. I would counter that you’re unlikely to be considered for positions using DL unless you’re pursuing your PhD in it, or have proven yourself in industry. Since that isn’t your situation, I’d wait until you got your foot in the door somewhere and then pursue DL on the side. That’s what I did, and then you look like a hero to your boss. This strategy led to my first publication in the field and I’m now working on DL almost exclusively.
Edit: one more thing. Think carefully about the type of work you want to do. My advice is assuming you’d like to be a person that trains/deploys ML models to solve problems in industry. This is much different than an ML Engineer, who’s implementing algorithms in low level languages and squeezing out efficiency. Obviously that would require a much deeper understanding of SWE. And a totally different person is an academic researcher that’s developing theory or technique. It’ll be hard to do that without a PhD.