Finding Pukei-Pukei
You are on the right track. Following tracks and clues is the way to find new monsters. Pukei-Pukei being no different.
Without directly giving you his initial location (because to me that spoils the fun). The Ancient Forest is a very large map, but Pukei likes the lower, more damp portions of the map. You can find your first trail once you head inwards into the jungle and swampy areas.
If you are absolutely frustrated and just want to know exactly where this guy is...
Area 6, the northeast most corner of the ancient forest, with the poison flowers.