Create or use an Apple ID without a payment method: https://support.apple.com/en-us/HT204034
However, you need an Apple ID to use the App Store. It's not needed for any of the built-in apps, though.
(It might be needed for iMessage or FaceTime? I'm actually not sure. I think you can use iMessage without it, but it doesn't sync between devices.)
Create or use an Apple ID without a payment method: https://support.apple.com/en-us/HT204034