Sirius and Ginny would have became friends because they both couldn’t sleep at Grimmauld Place. Like, one night after Ginny had a nightmare about her first year and Voldemort, she came down stairs to the kitchen and finds Sirius there because he couldn’t sleep because of nightmares about James and Lily and Azkaban. And at first just sitting there in silence not really knowing what to say to each other because they don’t really know each other. But then, they got to know each other and swap stories about themselves and became great friends, Ginny reminding Sirius of James, and Sirius just being a funny guy and understanding Ginny about the nightmares. And them just being great friends sitting in the kitchen helping each other with their nightmares even though they didn’t really talk about them. Just the other’s presence was enough to lessen the nightmares.