(How to) Ride the Shinkansen from Tokyo to Kyoto

I’m at Tokyo Station (at 6am) to ride Japan’s bullet train to Kyoto this morning. I don’t have a JR Rail Pass but I do have 15 minutes to get on the train! I also want an ekiben (train bento or boxed lunch) and A SEAT ON THE TRAIN!
I will buy a NON-RESERVED TICKET from a vending machine.
The bento shop is on the way. It’s time to RUN!!
(Can I get both in time?)