Hello ZN231,
Thank you for using Apple Support Communities. Sounds like you're experiencing issues creating an Apple ID for a child. Specifically, the process never completes, not allowing you to continue. If so, we'd like to recommend some steps you can try. Let's follow the steps below:
1.) Close the Settings app: Close an app on your iPhone or iPod touch - Apple Support
2.) Refresh things by restarting your iPhone: Restart your iPhone - Apple Support
If your issue continues, try testing this issue using a different device. For example, you can even use a Mac to create an Apple ID for a child: Create an Apple ID for your child - Apple Support
In macOS Ventura or later
1. Choose Apple menu > System Settings, then click Family.
2. Click Add Member.
3. Click Create Child Account.
4. Follow the onscreen instructions to finish setting up the account. Be sure to enter the correct birth date — you can't change it later. For your child's Apple ID, you can use their email address or their Game Center nickname.
In macOS Monterey or earlier
1. Choose Apple menu > System Preferences, then click Family Sharing.
2. Click the Add button
.
3. Click Create Child Account.
4. Follow the onscreen instructions to finish setting up the account. You can use the child's email address for their Apple ID, or their Game Center nickname. Be sure to enter the correct birth date — you can't change it later.
We hope these steps are helpful. Thank you for using Apple Support Communities. Take care.