It is definitely possible to become a NP even younger than 30. It seems like most NP programs require you to have worked as an RN at least a year before becoming a nurse practitioner. I have seen a few that require 2 years. Some, like Georgetown, don't require any experience but I have heard that it helps greatly in getting accepted to the program. If you think about it, while experience does help, the NP job is not the same as a RN. The best thing to do is to look at the programs you might be interested in and see what the acceptance requirements are.
Of course the more experience you do have, the better.
Most PA students aren't really required to have actual 'working' healthcare experience when applying to their programs and neither are pre medical students when applying to medical school. They need to have volunteered somewhere to get exposure to patient care for a certain amount of hours. Some do have an actual job like CNA or EMT. I have met a few RNs now through my online group that are also going for MD programs. The NPs, PAs, and MD/DO students learn what they need to know to work within their scope of practice in their degree programs and through their clinicals/residencies.
I have researched this a lot lately and even started some courses toward a post bacc pre-med since there seems to be no RN jobs, (even for BSNs) in the Jacksonville area. I am not even a new grad but a returning RN BSN who took time off for family responsibilities and did a refresher course with clinicals, mostly in a busy ICU. Things sure are tough out there for nurses.