You can find dig sites by finding either blue circles on the ground
or by finding small black circles that looks like scorch marks
However, the easiest way to get this is to wait until you meet Kai.
You'll be sent on a mission to retrieve some parts from green spiders, and your objective marker will be a spot with a ton of dig sites. The goal of the mission is to destroy a spider, but what you want to do instead is extract their cores so they don't drop the parts. Dig sites keep "spawning" until you get the quest item, so if you just keep extracting cores you'll eventually get enough to get
and
This is also an easy spot to farm the following achievements: