Trains are so frequent that you should be able to get a ticket after you arrive in Tokyo.

A look at Hyperdia tells me that there are Nozomi trains from Tokyo to Hiroshima every twenty to thirty minutes throughout the day. Unless you're traveling during a holiday period, you should be able to buy a ticket for your desired time.

There's a JR office at NRT, so you can check with them immediately upon arrival if you're worried. Even if you can't get a Green Car ticket (unlikely), the second-class cars are just fine.