What happens when you try to use it?
Read this document: What is Sign in with Apple? - Apple Support
Also note it says, "Sign in with Apple is not available for children under 13 years old. This age may vary by country or region." Maybe you don't qualify in your country?
If an app or feature on your device is not working, it may have been disabled using Screen Time, or by an IT administrator if you are using a device owned by an employer or educational institution. See how to use Screen Time on an iPhone, iPad, or iPod touch by clicking here --> Use Screen Time on your iPhone, iPad, or iPod touch - Apple Support
Perhaps ask Apple about this?
Click here --> Choose your country or region - Official Apple Support Select your country, then a product. If you don't see one that handles your issue then keep experimenting with selections until you reach one that gets you a chat session or a telephone call and get the representative to redirect you.
or:
"See a list of Apple phone numbers around the world."
Click here --> Contact Apple for support and service - Apple Support