The Alpine Linux documentation assumes you have a way to access your system directly, such as via a display and keyboard. However, there are many cases where you might want to deploy a headless box, such as on a Raspberry Pi connected via ethernet (or wifi).
There are instructions out there for how to install Alpine Linux on a Raspberry Pi, including how to deploy on a headless Raspberry Pi, but I found them to be somewhat out of date and inconsistent.
This repo packages the overaly file in a repo for version control. The full instructions are in the Alpine Wiki instructions.
Thanks for the original instructions from the Alpine Wiki user sodface, who also hosted the overlay files on their website (download). I expanded and updated these instructions and then added them to GitHub so they can be easily accessed.