Hi Calvin and welcome. The serial SHOULD be stamped into the polymer just below the slide on the left side(muzzle away from you) right above the trigger of the gun. Picture here : https://limitlessamerica.com/taurus-g3-t-taurus-optic-ready-option-4-barrel-9mm-thumb-safety-black/

The serial number of a Taurus gun is stamped into the polymer just below the slide on the left side of the gun, directly behind the slide lock1. The serial number is required to be on the frame of the gun, and it will always be there