In a small bowl, gently toss the cooked sushi rice with the rice vinegar and sea salt until the rice is well-coated and slightly sticky.
Slice the sushi-grade salmon into long, thin strips and slice the cooked shrimp in half lengthwise.
Julienne the cucumber into thin matchsticks and thinly slice the avocado into long pieces.
Place one nori sheet on a bamboo sushi rolling mat, shiny side down.
Spread half of the seasoned rice evenly over the bottom two-thirds of the nori sheet, leaving the top third bare.
Arrange the salmon strips, half of the cucumber, and half of the avocado in a horizontal line across the center of the rice.
Roll the nori tightly from the bottom using the mat, applying gentle pressure to secure the roll, and moisten the top edge of the nori with a drop of water to seal it.
Repeat the process with the second nori sheet, using the cooked shrimp and the remaining cucumber and avocado.
Using a very sharp, damp knife, slice each roll into 6 to 8 even pieces.
Serve the fresh sushi rolls immediately with coconut aminos, wasabi paste, and pickled ginger on the side.