Where's my "starting" pet?

When I started game first time, I found a pet in the very beginning - a “yellow quality” dog. I deleted that character (decided to play another class), and when I start a new character, I can’t find this pet. I tried restarting over and over again - no pet. Maybe I’m doing something wrong? Or I just was extremely lucky that first time?

The pet happens as part of the tutorial, once you play the tutorial level you cannot go back there.

Thank you for the explanation.

You are welcome. There is an enemy in the game called the “Enslaver”. They have pets with them. If you defeat these enemies it will drop the pet for you to pick up.