Preheat the oven to 150 degrees C.

Bring water to a boil in a medium pot; stir in rice. Reduce heat to medium-low, cover, and simmer until rice is tender and water has been absorbed, 20 to 25 minutes.

Mix rice vinegar, sugar, and salt in a small bowl. Gently stir into cooked rice in the pot and set aside.

Lay nori sheets on a baking sheet.

Heat nori in the preheated oven until warm, 1 to 2 minutes.

Center 1 nori sheet on a bamboo sushi mat. Use wet hands to spread a thin layer of rice on top. Arrange 1/4 of the crabmeat, avocado, cucumber, and pickled ginger over rice in a line down the center. Lift one end of the mat and roll it tightly over filling to make a complete roll. Repeat with remaining ingredients.

Use a wet, sharp knife to cut each roll into 4 to 6 slices.