Boil the noodles according to the package directions. Drain and return them to the pot.
Meanwhile, in a small bowl, whisk together the sugar, soy sauce, and lime juice.
Gently press the tofu slices between layers of paper towels to remove excess liquid, then cut into ½-inch pieces.
Heat the oil in a large skillet over medium-high heat. Add the carrots, bell pepper, and ginger and cook, stirring, for 2 minutes. Add the tofu and bean sprouts. Cook, stirring, until the vegetables are slightly tender, 3 to 4 minutes.
Toss the noodles with half the soy sauce mixture and cook over medium-high heat until heated through, 1 to 2 minutes. Transfer to a platter and top with the vegetables and the remaining soy sauce mixture.
Sprinkle with the scallions, peanuts, and cilantro, if desired.