The story you described is the premise of "Pacific Rim: The Black," an animated series set in the same universe as Pacific Rim, directed by Guillermo del Toro. In this series, the Kaiju, massive monsters that emerge from breaches deep in the Pacific Ocean, have overrun Australia, forcing humanity to evacuate the continent. The Jaegers, which are colossal, human-piloted robots, were built to combat the Kaiju, but their efforts fail, leading to the abandonment of the region.
The teenage siblings, Taylor and Hayley Travis, are left behind when their parents, Jaeger pilots, depart to fight the Kaiju and never return. Five years later, Hayley discovers an old training Jaeger named Atlas Destroyer. Along with her brother Taylor, they activate the Jaeger and embark on a journey across the ravaged continent in search of their missing parents. Along the way, they must not only battle the dangerous Kaiju, but also contend with other survivors who seek to take control of Atlas Destroyer for themselves.
The series explores themes of survival, family, and the human struggle against overwhelming odds in a post-apocalyptic world.