Booking a Green car Seat

Given we land during golden week on April 29th from Canada, can we book a shinkasen to Hiroshima next day before we exchange our voucher on the 29th?
Many thanks

You must first exchange the voucher before any booking using the pass. The pass has to be stamped by the ticket agent and he then writes the date that particular ticket was issued on the actual pass. If you have many reservations, your pass will be filled with little stamps by the time you're done.

As John mentioned, though be aware that you must have the Green Car JR pass.

Ordinary JR pass will not cover the cost of green car seat. For details, http://www.japan-guide.com/e/e2361.html

I may be wrong - but I do believe that it is possible to purchase a Green Seat ticket only before you even get your JR Normal Rail pass stamped.

This is because train tickets are split into two prices.

1) Basic train fair
2) Seat fare (including green seat surcharge).

Do note that the seat fare including green seat surcharge may be even more expensive than buying the basic train fare and seat fare for many journeys.

Others should confirm what I have said before you take it as gospel.