Apple - How to activate new iPad without disclosing credit card number?

I think you are going to need an iTunes account, but you can get around the need of a credit card. You can follow Apple's support documentation on how to setup an iTunes account without a credit card. You can use a Mac to make a free account that works on iOS and iOS to make a free account that works on Mac. Once your iTunes store account is set up once, you might want to avoid creating a second one since they cannot be merged later.

• Creating an iTunes Store, App Store, iBookstore, and Mac App Store account without a credit card - https://support.apple.com/en-us/HT204034

You can use most of iPad's built-in apps without an Apple ID, such as Safari, maps, mail, camera. However, certain ones do require an Apple ID such as Facetime. You can create an Apple ID without a credit card by using an iTunes gift card, or following the URL in vcsjones' answer.

If you want to use the iPad without an Apple ID, select these options at setup:

1. Don't have an Apple ID or forgot it
2. Set Up Later in Settings
3. Don't Use

This is useful because you if enter your Apple ID at setup, it will automatically login you into iCloud and sync all your iCloud data. If you skip the Apple ID at setup, then you can enter it later for App Store downloads without syncing all your iCloud data.