app store and iTunes gift card

Yes, but if the child is under 13 you will still need to set up Family Sharing in order for the child to have an account, and the organizer will still have to enter a credit card. The child can pay for items with store balance in the form of gift cards but you will need to make sure there is no overage which will be charged to your card. You can set up Ask To Buy to ensure this, or use parental restrictions or Screen Time to block certain features..

Request and make purchases with Ask to Buy - https://support.apple.com/HT201209

Redeem App Store & iTunes Gift Cards, Apple Music Gift Cards, and content codes - hhttps://support.apple.com/HT201209

Use Restrictions on your iPhone, iPad, and iPod touch - https://support.apple.com/HT201304 - "You can use Restrictions, also known as parental controls, to block or limit specific apps and features on your iPhone, iPad, or iPod touch, including access to explicit content in the iTunes Store."

Use Screen Time to get insights about how you use your device - "With Screen Time, you can access real-time reports about how much time you spend on your iPhone and iPad, and set limits for what you want to manage." "With Family Sharing, you can share music, movies, apps, and more with family — and it now works with Screen Time. You can view reports and adjust settings for children in your family any time, right from your device."

https://support.apple.com/HT208982