If the gobernment was behind it, they wouldn't let the choosen one bastioner get through training in the first place. Also the Kaijuu was not coincidentally coming through in that training session. So they have some consciousness or aim of their own to atk specifically the protagonist. As of now she is more like a trouble magnet and if she were to end it, the gobernment would have put the light out before she even advanced to become a threat to the "operation".