Divorce could be initited by either parent, but they must be a legal resident of that state. If your ex already initiated divorce, that is where the jurisdiction stands.
You can try to give up your parental rights, but it does exclude you from paying child support. The child would have to adopted by the a new husband of your ex, to be excluded from support.
It sounds like you are already a 100% absent parent. In that case, there is no need to stay where you are (in fairly close proximity to the child). There are areas of employment all over the country that can provide a full time job, which would enable you to pay your support.