Stephanie's Father's Treecko was first seen when Max released the starter Pokémon in the Pokémon Center. Treecko followed Ash and Max after they went to get the Torchic that escaped. Ash had already released his Treecko and it was obvious that Treecko liked Ash's Treecko.
Treecko and Stephanie's Father liked each other from the time they met and he asked Nurse Joy if he could keep Treecko.