Cook the Rice: Prepare sushi rice according to package instructions; season with rice vinegar, sugar, and salt.
Slice the Veggies: Thinly slice cucumber and avocado into long strips.
Prepare the Nori: Place a sheet of nori shiny side down on a bamboo sushi mat.
Spread the Rice: Evenly spread a thin layer of seasoned rice over the nori.
Add Fillings: Arrange cucumber and avocado slices horizontally across the rice.
Roll the Sushi: Use the mat to carefully roll the nori and rice over the fillings, pressing gently.
Seal the Roll: Moisten the edge of the nori with water to seal the sushi roll.
Slice into Pieces: Use a sharp knife to cut the roll into bite-sized sushi pieces.
Serve with Dips: Plate and serve with soy sauce, wasabi, and pickled ginger for dipping.