I guess you will know it is working if you don't get an infection.
On the product insert it says:
Neulasta® (pegfilgrastim) or NEUPOGEN® (Filgrastim) may reduce your chance of getting an infection, but it does not prevent all infections. An infection can happen anytime your neutrophil counts are low. Look for signs of infection, such as fever, chills, rash, sore throat, diarrhea, or redness, swelling, or pain around a cut or sore.