The App Store needs a valid credit card or an Apple iTunes Gift card to enable purchases (even of free apps)

No way around that

Create an iTunes Store, App Store, or iBooks Store

account without a credit card or other payment method

Learn what to do if you don't want to associate a payment method with your iTunes Store, App Store, or iBooks Store accounts.

When you use your Apple ID to sign in to the iTunes Store, App Store, or iBooks Store for the first time, you're asked to enter a payment method so that you can purchase items from the store. Follow these steps if you don't want to associate a payment method with your account.

Apple recommends using only one Apple ID for all Apple features and services that use Apple ID. If you don’t remember if you have an Apple ID, we’ll help you find it.

A credit card is required to set up accounts for children. Learn more about Apple IDs for kids.

If you already have an Apple ID

If you've already created your Apple ID, you'll need to add a payment method when you first use it to sign in to the iTunes Store, App Store, or iBooks Store. But you can optionally remove the payment method after you sign in to the store. You won't be asked for a payment method again until you make your first purchase.

If you don't have an Apple ID

If you haven't created your Apple ID, follow the steps below to create one and a store account at the same time, without adding a payment method.

On an iPhone, iPad, or iPod touch

On a Mac or PC

On an iPhone, iPad, or iPod touch

1. Open the App Store, iTunes Store, or iBooks Store.
2. Choose any free app, song, video, or book.
3. Tap Get next to the item, then tap again to get it.
   
4. When you're asked to sign in with an Apple ID, tap Create New Apple ID.
5. Follow the onscreen instructions. When you're asked for payment information, choose None. See what to do if None isn't showing or you can't select it.
   
6. After you enter all of the information required, you'll be asked to verify your Apple ID by email. You must verify your Apple ID before you can begin using it. Didn't receive the email?

If you use Family Sharing, and you’re the family organizer, you can’t set your payment information to None. You'll need to use a credit card or debit card.

Create an iTunes Store, App Store, or iBooks Store account without a credit card or other payment method - Apple Suppor…

Please note that the method described above will only allow you to download free apps. If you want to purchase an app you will at least need an iTunes gift card, which can be purchased at number of retailers (e.g. Apple retail store, Target, Walgreens etc).

You followed, exactly, those instructions (Create an iTunes Store, App Store, or iBooks Store account without a credit card or other payment method - Apple Support) when creating a new account ? The instructions won't work on existing accounts (nor partially created accounts). I've just tried it and created a new account and was able to download a free app without giving payment details