What is the problem with a 1997 Grand Am GT if it taps when first started and smoothes out after the car run for a while?

What you are hearing is the lifters tapping. Lack of oil changes, using poor quality of oil,wrong viscosity, and dirty oil filters will cause this. The engine bearings may be getting worn as well.
Change your oil regularly with good quality products, add in some oil treatment like Lucas oil stabilizer to help keep things lubricated after the oil has drained down to the pan, that way the tapping at start up will diminish or go away entirely.