Unfortunately, once you Father a child, you have a legal duty to financially support that child -- a duty from which you can't just walk away. The only way to do what you want to do is to have someone else adopt the child and to step into your shoes, meaning that you would no longer be the Father and a stranger would take on that obligation. Unfortunately, the mother would have to agree to this as well. Your obligation to support the child financially has nothing to do with whether or not you see the child. You may just walk away and choose not to see the child, but you can't walk away from the financial obligation to pay support. All of this is assuming that you are the Father of the child. If you believe you are not, a paternity test will establish that fact and you could be relieved of the financial obligation.
The information is for general information purposes only. Nothing stated above should be taken as legal advice for any individual case or situation.
If you signed a paternity affidavit at the hospital and it made it's way to the office of vital statistics you are the father unless you contest paternity within certain time periods. As a father, you have equal rights. There is some debate about whether a 17 year old can sign a paternity affidavit etc. If you were to file a court action you might have a guardian ad litem appointed to assist you under RCW 4 because of your age. Skipping that issue, however, the most common scenario for young unmarried persons is that the mother may go on public assistance. A child support action is started and an order is entered that makes the father and adjudicated father and gives sole custody to the mother. In essence, the father gives up custody unless he or the mother seek a parenting plan/residential schedule. IF your question is not about custody - but, rather about paying child support - the answer is no you cannot escape financial liability if the child is yours and the mother or the state wants to collect support. Visitation or custody with your child is not linked to child support. The court will rarely allow a child “one” parent.
Courts are very reluctent to allow parents to avoid their future duty to parent children just because they don't like the idea of being a parent. You would have to file a Petition to relinquish and you could do it in Juvenile Court. However, there are significant problems in being able to get out of your responsibilities and it is unlikely that you would have success without an experienced family law lawyer who would be willing to assist you. Could be costly for you but your chance of success without the lawyer is almost zero.,