First of all, there is an EGS Zone in Homeworld Space, the EGS Star (more Information here: EGS | Elemental Galactic Services i recommend to read it!) Dont approach the EGS Star with a CV!!! You need a SV to get close to it!
But as RexXxus already said, you dont need to go there to get unguilty.
You need the proper Container for your Origin, press Tab and look in the Character Window what Origin you are.
This could be different from the Faction Origin. For example your Faction is an Alliance Faction but you self started on Lawless. For Alliance you need the purple container and the Epic Assault Rifle.
Read more about Origins here: https://forum.empyrion-homeworld.net/c/hws-guide/hws-story