Rinse the rice until the water runs clear, then drain for 5 minutes. Combine with water in a saucepan, bring to a gentle boil, cover, reduce heat to low, and cook for 15 minutes. Remove from heat and rest, covered, for 10 minutes. Do not lift the lid during cooking or resting.
Stir rice vinegar, sugar, and ¼ teaspoon salt until dissolved. Fold through the warm rice with a cutting motion, then spread across a wide plate for 10 minutes until warm but not steaming.
Heat the oven to 425°F (220°C) and line a rimmed sheet pan with parchment. Whisk all sauce ingredients together. Transfer 3 tablespoons to a separate covered cup and set aside as the finishing sauce.
Pat the salmon cubes dry and season with the remaining ½ teaspoon salt. Add to the remaining sauce, fold gently to coat, and arrange in a single layer on the prepared pan. Roast for 8–12 minutes until the center of a thick cube reaches 145°F (63°C) and the flesh is opaque. Start checking at 8 minutes.
While the salmon roasts, arrange edamame, cucumber, carrots, radishes, and green onions near the bowls. Dice the avocado just before assembly.
Divide warm rice among four bowls. Place salmon on one side, then arrange the vegetables and avocado in separate groups. Spoon the reserved finishing sauce over the fish and rice, then scatter sesame seeds, green onion, and optional nori on top. Serve immediately.