This almost exactly happened to me a few years ago.
A woman whom I didn’t know knocked on my door. I lived at the time in a large apartment complex and I knew most people so I thought I would tell her where the person she was looking for lived and she had a little girl toddler age with her.
I opened the door and after saying hello she pushed herself into my apartment just talking normally and said things like “I live here how did you get all of my stuff” “I own all of these things” I told her I lived there for years. I couldn’t really get away from her to call the cops because 1) it’s a small apartment and 2) I didn’t want to leave her alone in my house with a toddler when she was obviously not mentally healthy.
Finally my aunt showed up and thought I knew the woman so she talked kinda friendly with her but finally picked up how uncomfortable I was right then and asked me if I did so I told her no. My aunt ran downstairs to where my grandmother lived and told her. My gram got the woman into the hallway so I could finally call the police.
The two officers showed up seconds later and one actually knew the woman personally and knew she had done this multiple times before. They called the woman’s parents to pick up the toddler and the woman left. The officer that knew her said I could press charges if I wanted but that the woman had been heavy into drugs before then and mentally affected her so it wouldn’t really go anywhere if I did.
The funniest part? While the cops were there, one of them glanced at my door and noticed the peep hole, then looked at me and said “You see that peep hole? I suggest you start using it.” He sounded sarcastic, but he might have been making a serious suggestion for my future well-being.