Norton Family setup can be done in two ways.
You can use the Norton Family client (Installed on the PC) or you can use Norton Family portal (https://family.norton.com/) to setup your child account.
To setup Norton Family on the device, Please click on Norton Family 'TrayIcon' and click on "Edit Accounts".
It will ask for account credentials, once you login you can configure Norton Family for any windows account.
Please try this and let us know whether you are able to setup for the desired account.
Moreover, you mentioned like 'you don't want to administer family options logged in as a child account'.
Norton Family is a parental control product and we recommend it to be configured for your child account so that your child can be safe online.
Please let us know if you need any further details, we will be happy to assist.