Ipad is looping at two factor verification when setting up child account

A child’s AppleID must be established from an adult’s (Family Organizer) Apple device.

Create an Apple Account for your child - Apple Support

Then the child’s device can be setup with the adult-created credentials.

Other references of relevance:

Set up Family Sharing - Apple Support

Use parental controls on your child's iPhone or iPad - Apple Support

Move a child to another group using Family Sharing - Apple Support

So the only way to create a child account is on the parent's Apple device? Well that's a bit rubbish and presumptious.

I don't have a Mac, iPhone, or iPad - nor do I want any of them. What I do have is an iPhone my 13 year old daughter insisted on buying and an endless 2 factor authentication loop trying to create a child account (it hasn't asked me anything about her actual account yet.

Sorry, but this brings back all the reasons I dumped Apple for Android over 10 years ago.

Sorry you feel that way.

Apple has a very good, well-conceived, and tightly integrated ecosystem to allow appropriate parental control, management, and oversight of children’s phones.

If a parent doesn’t become the CRITICAL part of that ecosystem, then choosing an iPhone for a child is — IMO — ill-considered.

Apple accepts returns for refund for 14 days.

Sorry.

Parenting’s challenging. Get used to it.

(My own are now adults)

Thanks for your opinion and your evaluation of my parenting skills. Not exactly constructive or helpful.

This is a cloud based issue and there is no technical reason beyond maintaining a walled garden that this be restricted to Apple devices.

I never intentionally criticised your parenting skills; only acknowledged the challenges you’ve likely already encountered — and with a 13 yo — still have ahead.

Your “walled garden” concept is spot on; only Apple’s walled garden is based on their fundamental architectural construct of “Trusted Devices”. (If you’re using a Trusted Device … you can then be “in the garden”)

Best of luck going forward.