I don't think you realise how damaging this is going to be for your baby. Identity is a big part of growing up, you need to find out for her mental health and development who the Father is.
This isn't your big secret to withhold. Are you seriously planning on saying to this child, I just don't know? Or there's these options, I could have found out when you were a baby but decided I didn't want to.
This is from knowing a person who is an adult, who doesn't know who their father is. The Mother simply refuses to divulge.
Not really sure how the legal system works. I'm fairly sure you could find out, then take measures to initiate or deny access. Unless around the time of ovulation you had a different man every night, you must have a vague idea.
In 5/10/15 years you might not be able to find all parties, that will cause further trauma. Life isn't as black and white as, it's my choice, I'll do as I please.
I hope you take this in as the person I know has been to hell and back trying to find out. You wouldn't believe how much identity means to an individual, until they are stripped of it.