Rinse the sushi rice in cold water until the water runs clear. Place the rice in a rice cooker with 2 cups of water and cook according to the manufacturer's instructions.
In a small saucepan, heat the rice vinegar, sugar, and salt over low heat until the sugar dissolves. Set aside to cool.
When the rice is done, transfer it to a large mixing bowl. Pour the cooled vinegar mixture over the rice and gently fold it in using a wooden spoon or rice paddle. Cover the bowl with a damp cloth and let it cool to room temperature.
Open the inari-age and gently remove any excess oil by blotting with a paper towel.
Stuff each inari-age pocket with a small amount of rice, making sure not to overstuff them. Fold the top of the pocket over to seal.
Arrange the stuffed inari-age on a serving platter.
Top each inari-age with julienned cucumber, carrot, avocado, and pickled ginger.
Serve with soy sauce or tamari on the side.