Is Child Support Retroactive If Parenthood Was Never Determined? Please Help.

I've potentially had a child with a girl in early 2019 in Seattle WA, she put restraining order on me while she was 2 months pregnant but in court documents said i was father. I've noticed this 3 years later because she never told me she was pregnant i only noticed after carefully reading entire court related documents after having case dropped years later due to SOC deal. I contacted her after and asked if he is mine, she would always say that he's hers actually. I just said i want to be there if he's mine and would give her thousand dollars a month voluntarily. Then i would ask if i can sign his birth certificate and she would not let me and change topic, i asked for dna test and she would not let me. Basically i could only see him couple hours a week and that's it, sometimes whole weekend. I could not get his paper documents, i could not travel with him and she absolutely does not allow me to take him to a doctor as she is extremely against vaccination.

A month ago however, i vaccinated him anyway because he was coughing really bad one night and we could not sleep at all. Then she stopped letting me see him. She does not want to go to court as mostly likely she thinks i will get parental rights and also vaccinate him. She says one day she will take me to court and get all the retroactive years of pay. Child is turning 7 in a month and i've given her around 20k over on and off contact with her in last 3 years. 1k a month and 3k one time. all through zelle.

I'm just tired and i don't know if i should go to court and spend potentially tens of thousands to chase someone who potentially might not even have my biological child.

Location: Seattle, WA