I can flesh these ideas out more, but so far what do you think?
The Detective
An ex US soldier now Tokyo Detective James Banks has been through a lot in his life. Fighting for his country only resulted in retreat and abandonment by his own government during the Great Gastrea war. Every town they fell back from to let it get swallowed up by the horde of Gastrea only for his own unit to be sacrificed made him feel far less devoted to his country. Leaving the country when the war was over wasn't easy, but his friends and family was destroyed by the war and for awhile he blamed his leaders for it. Moving to Japan wasn't the worst idea for him since he did want to go there even before the conflict. Trying to make a living for himself there was hard, but eventually he was able to join the police force and even become an up and coming detective.
Alright I can add more to it, but the gist is James is a detective in the Tokyo Area. He's skilled enough to be a promoter, but after what happened in the war he isn't too wiling to fight Gastrea again. Not sure exactly how he can get involved in the story yet. He could find a cursed child being abused by cops and stop them then try and take care of her. Maybe because of that he thinks about becoming a promoter so she can get better care?
The Cursed child
Akane wouldn't consider herself anything special. She was abandoned by her parents at birth, but was lucky to be given to a good family who specialized in raising cursed children. It still didn't matter to her since all she really learned in the past 10 years was that most people think she's a monster and is responsible for all the world's problems. That itself always caused her to feel inadequate and even inferior a great deal of the time. Her own feelings were simply a mixture of rage and sadness. However, that didn't stop her from defending her friends from some humans who decided they needed to be taught a lesson. Akane always saw the other girls who lived with her as family, and when some gunman shot at them simply for being at the wrong place at the wrong time she snapped and killed almost all of them. All of the pent up anger was released at that moment. Eventually the police tracked the murders and assumed it was likely the fault of one of the cursed children in her family. Eventually they were all taken away and split up. Akane was the lucky one and was found by a Promoter from the Civil Service Agency who was recruiting.
I can go into far more detail, but for now that is it. Akane can easily be extremely emotional and shy a great deal of the time, but when it comes to fighting she is reckless. Anger almost always takes over and leads to unnecessary amounts of collateral damage.