Season the cooked sushi rice by gently folding in the rice vinegar, coconut sugar, and sea salt until well combined.
Slice the fresh sushi-grade salmon into long, thin strips and cut the cucumber and avocado into slender matchsticks.
Place one nori sheet on a bamboo rolling mat with the rough side facing up and the lines running horizontally.
Wet your hands and spread half of the rice in a thin, even layer over the bottom two-thirds of the nori sheet.
Arrange half of the salmon, cucumber, and avocado in a horizontal line across the center of the rice layer.
Roll the nori tightly from the bottom using the mat for support, then seal the top edge with a small drop of water.
Repeat the process with the second nori sheet and remaining ingredients to create two full sushi rolls.
Use a very sharp, damp knife to slice each roll into eight even pieces and serve immediately with tamari and wasabi.