More than likely, you have a hydraulic lifter that has leaked down and may be fouled with dirt or other material that has built up over the years. When you first start up cold, there is a very short period (3 to 5 seconds) needed for the oil pump to repressure the system and pump up the lifter. Though you may find the tapping noise objectionable, you are not doing any measureable damage to the engine to leave it "as is". You can add some solvent (many commercially available solvents out there that profess to clean up "dirty" engines), or replace the the lifter (a nice project for a DIY person).