How can I verify my age without a credit card or photo ID?

You haven't told us where you are located. Refer to these support articles and also reads the tips and suggestions in the link at the bottom.

Here are support articles covering age verification requirements that are being implemented in several countries:

If you’re asked to confirm that you’re an adult - Apple Support

Region-specific rules for managing an Apple Account - Apple Support

Age requirements for Apple Accounts in the UK —> Age requirements for managing an Apple Account in the UK - Apple Support

More about the UK —> Age verification is stuck for 3 days in A… - Apple Community

Community threads outlining age verification in the UK and troubleshooting tips:

iPhone not accepting ID for age verificat… - Apple Community

Can't confirm age in UK - Apple Community

Age requirements for managing an Apple Account in South Korea —> Verify your age when you download or stream mature content in South Korea - Apple Support

Age requirements for managing an Apple Account in Singapore —> Age requirements for managing an Apple Account in Singapore - Apple Support

For further assistance:

You can reach Apple Support here: https://getsupport.apple.com/

You can also find the support phone number for your region at this link: Contact Apple Support - Apple Support

Re: “I have none of those.”

Maybe it’s time to obtain one.

If in the U.K., those are your current options.

If you are in the UK, you have these choices:

• Drivers License
• Credit Card
• Passport
• TOTUM card
• MyID Card
• CitizenCard
• NYSE Card

Age requirements for managing an Apple Account in the UK - Apple Support

Without verification you will be restricted from accessing websites with adult content and images that contain adult content that are sent to you will be blurred.

17n7 wrote:

I have none of those

If you are in the UK, then you should expect restrictions on your device to comply with the UK law and prevent content from being displayed that they have determined may be harmful to those that cannot prove they are an adult.

Apple has chosen those 7 types of identification to do that and in some cases are able to verify themselves when an Apple Account has been created at least18 years ago, which would mean you are now an adult.