Prepare sushi rice according to the recipe instructions and let cool to room temperature. Drain and pat dry tofu. Using a cheese grater on its side, shred the tofu. With the pieces that break off and are too small to grate by hand, use your fingers to tear them into smaller pieces. (you will need about 1 + 3/4 cups of shredded tofu).
Add grated tofu, vegan mayo, ketchup, hot sauce, and salt in a medium bowl. Stir to combine. Set aside.
To prevent the rice from sticking to the mat and make clean-up a breeze, wrap the bamboo mat in plastic wrap and use scissors to cut the whole nori sheet in half, creating two half sheets.
Lay a half sheet of nori horizontally on your bamboo mat, with the rough side facing up and the shiny side facing down. Dip your fingers in a small bowl of water, then use your wet fingers to take some sushi rice and distribute it evenly over the nori sheet, leaving approximately 1/2 inch of the top portion uncovered.
Flip the nori sheet over so the rice faces down and the bare top part is now at the bottom. Position the tofu crab filling and avocado slices across the center of the rice layering in the middle of the sheet. Be mindful not to overfill your sushi roll, as this will prevent it from properly sealing.
To roll the sushi: Lift the edge of the nori closest to you and tuck the bare flap of the nori inside the roll. Roll until you've completed the roll. Using the mat, give a firm hug/squeeze the roll with both hands. Repeat to shape the roll further.
Decorate with sesame seeds and vegan caviar (optional), cover with plastic wrap tightly, slice into six even pieces using a wet, sharp knife and serve with soy sauce, wasabi, and pickled ginger.