First, I went through the Recurse Center, which is a 3 month program sort of like a writing retreat for programmers. I learned a lot about Python and AWS in that time, and got an internship as a data engineer.
In that Fall, I started a computer science master's. I've taken mostly courses in machine learning including: Machine Learning Theory, Deep Learning, Probabilistic Graphical Models, NLP, and GPUs. I've collaborated with two professors on research papers, which has definitely been the highlight of my degree although I definitely think the courses were necessary as I continue to use the information that was covered.
Finally, I'll be starting this summer as a research engineer doing deep learning! This process took me 2.5 years, but I feel very prepared for my new role. It probably is possible to do this faster by joining a program like Metis or Insight, which prepare you for data science like jobs w/in 3 months. I would say that approach is slightly more challenging / high risk. If you really want to go into machine learning, I'd say doing the degree is a more surefire approach, granted it's more expensive in time and money.