Tsukigami no Ichizoku can be challenged for the first time after you beat Destructchers. When you return to the Inazuma TM Caravan, you'll meet Garsha, who'll say that he wants to confront the team that beat The Lagoon. He'll then give you the item to be used as an artifact to arrive at Ichizoku's hideout. The team level will be around 70. After beating them, you can recruit them at the Cretaceous period.