How can I download apps without the verification requirement?

It is not possible.

You may need to have a payment method on file, even if the app you want to download is free.

👉 Sign in to your Apple ID account page and edit / update your Apple ID details.

https://appleid.apple.com

On the Sidebar click Payment methods -> then tap Payments Methods and tap Manage payment method.

Or -> Change, add or remove Apple ID payment methods

https://support.apple.com/en-gb/HT201266

See also -> Payment methods you can use with your Apple ID

Payment methods you can use with your Apple ID – Apple Support (UK)

You can also use your Apple ID balance as payment method:

Add money to your Apple ID balance

Add money to your Apple ID balance – Apple Support (UK)