Press the tofu for 15 minutes to squeeze out the extra liquid. You can use a tofu press or slice the tofu into two flatter slabs and line them with a kitchen towel before placing them under a heavy cast iron pan.
Meanwhile, cook the rice and steam the edamame according to their package instructions. Make the tofu marinade by whisking the teriyaki sauce, garlic, and ginger together.
Slice the tofu into 1-inch cubes and place them in a shallow dish that has a fitted lid. Drizzle the marinade over the tofu, close the dish, and flip it over every once in a while as it marinates for 15 minutes in the fridge.
Prepare the other ingredients by cutting them into bite-sized pieces.
Make the aioli by whisking together the vegan mayo, lime juice, minced garlic, sriracha, and sugar.
Assemble the poke bowls by adding the grains to the bottom. Then add the vegetables, fruit, and tofu. Drizzle the sriracha aioli and any leftover marinade over the bowls. Garnish the bowls with sesame seeds and seaweed.