Rinse the sushi rice thoroughly and cook according to package instructions, then season with rice vinegar and let cool to room temperature.
Slice the sashimi-grade salmon into long, thin strips approximately half an inch thick using a very sharp knife.
Peel, pit, and slice the avocado into thin wedges, and julienne the cucumber into matchstick-sized pieces.
Place a nori sheet on a bamboo rolling mat with the rough side facing up.
Wet your fingers slightly and spread half of the cooked rice in a very thin, even layer over the bottom two-thirds of the nori.
Arrange half of the salmon strips, avocado wedges, and cucumber matchsticks in a horizontal line across the center of the rice.
Using the mat, roll the nori tightly from the bottom up, applying gentle pressure to create a firm cylinder, and repeat for the second roll.
Use a damp, sharp knife to slice each roll into 8 even pieces and serve with coconut aminos, wasabi, and pickled ginger.