So, normally I would say you should simply go to Tokyo station and get on the shinkansen to Kyoto, which would be easy to do and would not require advance reservations for a weekday afternoon.

However, this is in the middle of Golden Week, so I'm not so sure - I suspect many people will take May 1st and 2nd off (as they are not holidays....) and they will be traveling in advance so trains might be empty then.
In theory, it should be possible to go to the JR office at Narita airport and have them get you tickets from Narita all the way to Kyoto (presumably taking the Narita Express and changing trains at Tokyo Station); however, I suspect any sort of JR office at Narita airport will be a mess and full of people (the offices at most stations are consistently crowded.....).