We work hard exactly so that you can run Phoenix in production and gradually learn more about the BEAM along the way!
One recent example is the built-in dashboard showing all the different data the VM and the framework provide: https://github.com/phoenixframework/phoenix_live_dashboard/ - at first it may be daunting but providing a web-based experience to help familiarize with the building blocks is hopefully a good first step. We also added tooltips along the way to provide information about new concepts.
The same applies to Elixir: learning all of functional programming, concurrent programming, and distributed programming would definitely be too much to do at once, so we do our best to present these ideas step by step.
For what is worth, this is also true for Erlang. It has tools like Observer (which was used as inspiration for the dashboard) and a great deal of learning materials.
One last advice is to not drink the cool-aid too much. For example, you will hear people talking about not using databases, about distributed cluster state, etc, and while all of this is feasible, resist the temptation of playing with those things until later, unless the domain you want to use requires explicitly tackling those problems.
I hope this helps and have fun!