I know this is a broad, perhaps off-topic question but please bear with me.
I graduated 4 years ago with a degree in Mathematics (but didn't take many Statistics courses). It was only after a few years of working in a non-related field that I discovered my passion in Data Science. I decided to quit my day job to focus on learning all the necessary skills needed to be a data scientist. It became very apparent however that there are many concepts to learn and it is not going to take a short time to catch-up with the competence of the typical professional data scientist that has a PHD in statistics. Data science an interdisciplinary field requiring strong competence in Computer Science, Stats, Math, Economics, Psychology and so forth, but despite this, I have started (6 months) immersing myself in lots of content such as conferences, lectures, PDFs, CV questions and answers to attempt to bridge this gap, and I am incrementally learning more new stuff.\
I guess my question is, what is the best way to approach a career in this field? Should I take the approach of getting an entry-level job as a Data scientist and "learn on the job", or rather dedicate a year (the length of a Master's degree) to immersing myself in high quality content, then applying for a job? I read many answers on CV, and find myself admired by the level of competence that many reputable users have here, and thinking that there is still a long way to go.
Any advice — greatly appreciated.