Rinse rice in a sieve under cold water until water runs clear, about 1 minute. Bring rice and water to a boil over medium-high heat in a saucepan. Reduce heat to medium; simmer, covered, until rice is tender and water is absorbed.

Whisk together vinegar, sugar, and salt in a bowl until dissolved. Drizzle vinegar mixture over hot rice, fold gently, and let rice cool to room temperature.

Halve cucumbers lengthwise and cut each half into 4 pieces. Trim peel sides to sit flat. Scoop out seeds to form boats with about a 1/3-inch border.

Spoon 1 to 1 1/2 tablespoons of rice into each cucumber piece. Compact rice gently. Top with salmon, avocado, and sesame seeds.