Hello, I will be traveling to Japan in August. I would like to take the "Thunderbird" train from Kanazawa to Osaka. This is my only train trip so I do not need a JR Rail pass. Can I book the tickets in advance from America? If not, is it easy to buy the tickets in Japan, and is there a danger that the trains will sell out?

No, you cannot book those tickets from the US. It is very easy to buy your tickets in Japan. You can buy them at the train station the day of your trip to you can buy them in advance from the train station.

Thank you!!!

https://www.seat61.com/Japan.htm

I recently did the opposite, Okayama to Kanazawa and transferred in Kyoto to take the Thunderbird. Had to run for our lives to make the Thunderbird as we had reserved seats. The platforms were very far apart. I think we had less than 15 minutes. If you need to transfer to continue to Osaka, I would allow at least 20 minutes between trains and try to find out your next platform, if you can, before leaving Kanazawa. We really enjoyed Kanazawa with the beautiful sakura blossoms.

I would expect to be able to get a reserved seat at the last minute or at least a seat in an unreserved car. But, I might buy it when I arrive in Kanazawa. You can get one sooner - in Japan, as Kathie explained.

An advance ticket would be a good idea if your travel date is on/near an Obon travel date. Aug 15/16, in particular as explained here: https://www.japan-guide.com/e/e2286.html

This is an easy trip with no change of trains. You can use the hyperdia link below to get a timetable. Just change the day of the month to your date and search again. Then click on "Interval timetable" for any one of the results. The popup window will show the timetable for the day.

Notice that some of the Thunderbird L'ex trains make more stops than others. The travel time difference between the 8:05 and 8:15 departures is 17 minutes. Not a big difference in time but the quicker one is better because the trip will be smoother without the several stops.

Ignore the "Seat Fee" amount on hyperdia. Your cost will be :¥ 7850 reserved or :¥ 7130 unreserved.

Here is the link
HyperDia | SearchResult

And here is the "interval timetable" that I mentioned. It is for Aug 1 but likely the same for your date.
HyperDia | Interval timetable

Thanks!!