The earliest Narita Express from Shinjuku leaves at 5:55 am and arrives at NRT T-1 at 7:18 am. For a 9:30 flight, that should be plenty early. Japanese airports are very efficient and there really is no reason to do the "3 hour" rule that American airports suggest. I might even be tempted to take the next N'Ex at 6:34 am, arriving at 7:55 am but I understand a first-timer might not be comfortable with that.

If you really want to get to NRT earlier, you would have to take the Yamanote Line to Nippori and take the Keisei Skyliner to NRT. That would not be covered by a JR Rail Pass and would be a rather complicated connection at Nippori with 7 minutes to get to the Skyliner platform. If I was really wanting to go that early, I'd probably skip the Yamanote and just pay for a cab to the Keisei-Ueno Station and catch the Skyliner #1, departing at 5:58 am, eliminating that nasty connection.

Really, that first N'Ex from Shinjuku at 5:55 am will get you there in plenty of time. If you don't want to get going that early, the other alternative would be to move the night before to an inexpensive airport hotel and let their shuttle get you to the airport in the morning.