My phone was stolen and find my phone was off, is there any other way to trace it?

Hello ~ There are still some things you can do though. Take a look here:

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

*protect your account if Find My was not turned on.

~Katana-San~

Sorry, no. And Apple does not get involved with tracking lost or stolen devices using the serial number or IMEI. You might try contacting your cellular provider but the major ones have similar policies.