Signing A Birth Certificate If I Am Unsure Of Paternity

Both my girlfriend and myself are residents of Georgia (the state) and are set to have a child born in Georgia in a few months. Note we are both unmarried and do not have any other kids.

I have some doubts about if I am the biological father of the child, but no proof of any infidelity.

In order to not upset my girlfriend I intend on signing the birth certificate and acknowledgement of paternity. After which I will get a private DNA test to ensure that I am the biological father of the child.

My question is, if I am not the biological father, will signing the birth certificate or acknowledgement of paternity have any long term consequences? Will I be able to disavow paternity? Do I have a timeframe to do so? Will I be on the hook for child support?