Purchasing tickets without a JR rail pass

We are six people in need of round-trip tickets on the Shinkansen train between Tokyo and Nagano. We will be going in March in order to see the snow monkeys. Can we buy our tickets upon arrival in Tokyo? We would purchase them either on March 22 or March 23 for travel on March 24. We need to be in Nagano by 8:45 AM. Do these trains ever get booked up? The J R pass doesn't really pencil out as this will be the only day that we will be traveling by train other than a possible one way train trip between Narita Airport and our hotel in downtown Tokyo. I would love to buy these tickets in advance online but don't see a way to do it other than getting the pass. Thank you!

You can't buy them before you arrive in Japan. Once you arrive in Japan, you can purchase them anytime you want; I'd suggest doing it as early as possible, but I doubt the train will book out quickly. Just go to any JR ticket office (green with a symbol of a person reclining in a chair) in any major JR station.

Adding on: take the train information with you to make it easier (train name, time, departure and arrival station).

Some of the trains do get full, so book when you arrive in Tokyo (I've stood in a queue and watched the train I wanted sell-out), and that was a random non-busy day.)

Tokyo to Nagano can be booked online in English.

I would love to buy these tickets in advance online but don't see a way to do it other than getting the pass.

Actually, you can reserve your seats online (up to a month in advance) and pay for your tickets once you arrive.

https://www.jreast.co.jp/e/ticket/reservation.html

Thank you so much to all of you for your helpful responses!

Hi all, I will be getting a JR East Pass and would like to reserve the Narita Express to Tokyo and shinkansen seats to Sendai.
The website stated that the reserved tickets must be collected by 9:00 p.m. (21:00, Japan Standard Time) on the day before departure. That means I cannot reserve seats online for rides on the day of my arrival? So I can only reserve on the spot after I arrive at the airport?

There is no need to reserve tickets from Narita to Tokyo. The trains never fill up and, more importantly, you don't know which train to take. All trains from Tokyo to Aomori stop at Sendai, so there's no need to reserve that one either, as all trains will stop there. Plus, you don't know which train to take either, because of your first train.

All trains from Tokyo to Aomori stop at Sendai, so there's no need to reserve that one either, as all trains will stop there.

That's a very weird thing to say. If you are implying that "all trains stop at Sendai" means "it's always possible to get a seat", then it's false. It is totally possible that the reserved seat sections of all trains on a given day are booked out, but if that happens you can try your luck at an unreserved seat on a Yamabiko, or get a standing ticket on a Hayate/Hayabusa/Komachi.