Nothing better than the 808 kick as a first beatbox build, a solid foundation…
There are many designs around based on the original service manual published by Roland, including all the schematics.
https://archive.org/details/roland_Roland_TR-808_Service_Manual
I got help from this one, as the original schematics have been redone at a larger scale:
http://www.ericarcher.net/wp-content/uploads/2014/07/tr-808-bass-drum-diy-project.pdf
Just be aware that you are going to need a negative -12 or -15 Volts DC rail. I could build myself one using the negative edge of the pulse out of a 555 timer using this:
https://www.allaboutcircuits.com/projects/build-your-own-negative-voltage-generator/
This is how it looks on a breadboard:
And this is how it sounds: great!!