can you track an iphone with the serial number

No. We cannot.

To find a location of an iPhone it will have to be activated on the Find My app and then located from another device. For this to work the Find My activation on the iPhone has to be done before it is lost.

Axel F.

no apple product ever been able to be trace by serial number

pretty sure it would not be legal in most of the world

If your iPhone, iPad, or iPod touch is lost or stolen - Apple Support