Q.Can Sakura (桜) bloom in a small pot?
I have a small pot shown in the picture, and want to know if an Edohigan (江戸彼岸) type Cherry Blossom tree would be able to bloom flowers in it. The pot is being compared to a shoebox for a size 8.5 (US) shoe.

I do not believe that this variety would work for a container potted specimen.
Perhaps it would be available in Bonsai form. The container size you mention would be for a Bonsai tree.
Here are a couple of links to articles with more information:
https://www.gardeningknowhow.com/special/containers/how-to-grow-container-trees.htm
https://www.gardeningknowhow.com/houseplants/bonsai/bonsai-basics-starting-your-own-bonsai.htm