Sure!

     - Use the workflow_dispatch type so it can be manually triggered. Or schedule if you want it to run periodically.
     - Install dependencies like automake/cmake and libraries using brew (I cheat here a bit)
     - Clone the repository
     - Perform the steps for building a static build
     - Use actions/upload-artifact@v2 to upload the executable.

It's simple, although to get it right with some programs. The advantage is that with one click you can download it, put in your path, and it won't need special paths.

Here's an example with jq: https://pastebin.com/gHu8dTgQ

Honestly the best option is asking maintainers of each program to add a static build to their projects in order to make their projects able to run without installing dependencies. Problem is, some maintainers are very anti-static-compiling.