In a fine-mesh strainer, rinse rice under cold water until water runs clear. In a medium pot, combine rice, kombu (if using), and 2 cups water. Bring to a boil over high heat, then cover, reduce heat to low, and cook until liquid is absorbed and rice is tender, about 15 minutes. Remove from heat and let rice steam 10 minutes. Discard kombu. Fluff rice with a fork.
Meanwhile, in a small heatproof bowl, microwave vinegar, sugar, and salt in 30-second increments, stirring between each, until sugar and salt are dissolved.
Transfer cooked rice to a baking sheet, then carefully pat in an even layer. Sprinkle with vinegar mixture. Using a sushi paddle of flat wooden spoon, mix vinegar mixture into rice, cutting and folding rice over itself, trying not to smash or break any grains of rice. Cover with a damp tea towel until ready to serve.
Pat tuna dry, then freeze until just firm, about 5 minutes. Transfer to a cutting board, then thinly slice or finely chop.
Divide rice among bowls. Top with cucumbers, avocado, radishes, nori, and fish. Drizzle with soy sauce and spicy mayo. Top with pickled ginger and sesame seeds (if using).
