Welcome to OCDO. While I'm not familiar with how Goldsboro is with OC'ers, I'm fairly positive that you should be fine.
Don't know how long it takes that counties sheriff to give you a PPP either, but most counties in this state give them to people either that day or the day after. And for clarification, we have a CHP (concealed handgun permit) here.
Don't know what your schedule is like, but we're having a range day tomorrow (19th) at Paradise Hunting Preserve if you would like to join us. Check out the ENC Range day thread for more info