How do I check how old is my iPhone 13?

You can log onto checkcoverage.apple.com with your Apple Account and select your device or enter the serial number for it. It will tell you when the device was purchased.

There is no way of knowing that.

If you are the first owner: To know the purchase date of an iPhone, you need to look at the invoice date. It is not available on your device.

If you are not the first owner, what do you want to achieve by knowing the age of the iPhone is unclear to me.