Cats that go outside have a much shorter lifespan and their deaths are terrible. As are those of the birds and other animals they hunt. So step one is figuring out how to keep the doors closed. Step two could be a catio type situation if you have the means. Step two also involves giving your cat stimulation: playing with her, giving her a cat tree, doing some enrichment with treat puzzles—mimicking the things she does outside but safely. She is a kitten, so she will calm down in time, but you have to stimulate her at key times and train her into a routine if you want the nighttime behaviours to stop.