There is a setting that configures the Content Authors access to the Settings section (aka SiteConfig). The permission is set to false by default. I want to hardcode this setting to true so I don't need to manually set it to true after every SS install.

The setting is found in the CMS: Security > Groups > Content Authors > Permissions

Solved thanks to 3DGoo. You basically extend the Group Class.

mysite/code/extensions/CustomGroup.php

class CustomGroup extends DataExtension {

    public function requireDefaultRecords() {
        parent::requireDefaultRecords();

        $contentAuthorGroup = Group::get()->filter('Code', 'content-authors')->first();
        if ($contentAuthorGroup) {
            Permission::grant($contentAuthorGroup->ID, 'EDIT_SITECONFIG');
        }
    }
}

mysite/_config/config.yml

Group:
  extensions:
    - CustomGroup

Warning: this will reverse the setting. If it's on, it will be set to off, if it's off, it will be set to on.