Date & Time > Set Automatically is Greyed out.

It may sound weird and absurd but it is true and works...

When you find that the Date & Time feature is greyed out.

It is best to Set Screen Time Password Off and this will enable Set Automatic Date & Time

Watch this GIF below

Get help with the date and time on your iPhone, iPad, and iPod touch ...

https://support.apple.com/en-in/HT203483