Registering a child account under a new Apple account with only Mac

I have one Mac and no iOS devices. I have a new iCloud account and I want to create a child account within family sharing. I’m told by Apple support that this must be done by using the Settings app and clicking Add Member to create a child Apple Account within the family sharing group. The Add Member button simply sits there with a spinner and never begins the creation process. Is there another way to create the child account?