If you are born in Japan and stateless, can you have Japanese citizenship?

I'm asking because my aunt, she is Romani (Gypsy, not Romanian) and she gave birth to my cousin back in 2005 and she is stateless as a result of being Romani. She came to Japan when she thought she was going to get a job and escape the Czech Republic but really, it was just a scam to get prostitutes. She's been in Japan ever since (we went several years without knowing where she was). Her son, my cousin, was born in Tokyo before the scammers released her several months ago and he wasn't born in a hospital so no papers were filed on his birth. She doesn't know who his father is. She has no citizenship as I stated and she's very afraid to go anywhere for help because though she has had a horrible experience in Japan, she's terrified of going back to the Czech Republic. And especially being an unmarried Romani woman with a child, our family would just disown her and she'd be helpless. Can she and/or her son have Japanese citizenship considering they both are stateless and her son was born on Japanese soil? She has three women, who are all Japanese citizens, who did witness the birth of her son in Tokyo and are willing to vouch for her. There are even pictures of his birth and him growing up in Tokyo (two of the women who were present at his birth raised him until the prostitution ring let her go). Is that enough proof? Please help. Thanks.