If you are in undergrad, I'd recommend something like, Math or math-heavy science BS -> undergrad research -> computationally heavy PhD -> entry level DS or ML engineer job -> senior ML job (within a year or two) If you are older and looking to pivot, I'd recommend, Data engineer -> senior data engineer -> entry level DS -> senior DS
You don't need a PhD for DS/ML Engineer. Even at FAANG, even in their research labs. Usually a PhD is only in the requirements for Research Scientist (RS). That said, I did a PhD (and am now a RS). It's a fantastic opportunity to learn fully focused during a few years. But if your sole objective is the career (which is ok!), don't do a PhD. There are much easier ways to break into ML industry.
I had been working in Attitude Determination and Control and Optical Systems Engineering for seven years before that interview and I just like, knew the stuff from the job. I've been back on pure-SWE roles for four years already and I don't think I could do it now. I have the intuition but I couldn't white board proofs for tree based algos and manipulate integrals like I did on that interview for sure.