You and your boyfriend would have to file a Petition for Adoption and give your son's biological father notice of the Petition for Adoption. The biological father then has the opportunity to object to the adoption, or not. If he does not object, you can go through with the adoption. If he objects, you can litigate the adoption (and/or seek back child support)
Is there an open child support order, or are you referring to how much the biological father would owe if you filed for child support? Please note that if the biological father owes almost $30,000 in back child support, you do have the opportunity to file a Complaint for Contempt against him.
I would suggest contacting an attorney to discuss this.
Sign up to receive a 3-part series of useful information and advice about child custody law.