Prerequisite: After landing on Eos, enter the Research Center in Site 1: Promise.
This task is started after restoring power to the site and accessing the Research Center’s terminal. You just need to craft a new weapon using the readily available resources in the area. Just create something that doesn’t require too much resources that you don’t have. For example, for the sake of completing this task and earning EXP, just create a Disciple Shotgun or Mattock Assault Rifle since their materials are abundant in the immediate area.
If you want to get a better weapon at this point, you can go around and scour the site for objects that you can scan. It’s possible to earn enough research points to create a different weapon from the ones currently available as default.