Press the tofu for 15 minutes using a commercial press. Or wrap the tofu in paper towels and place it between 2 flat surfaces. Place something heavy on top.
While the tofu presses, make the marinade. Combine balsamic vinegar, soy sauce, green onions, ginger, garlic, maple syrup, and Sriracha in a small bowl.
After pressing, slice the tofu into pieces, about ¼ of an inch thick. Place them in a shallow bowl and add half the marinade mixture. Flip the pieces a few times to cover them. Marinate them for at least 30 minutes.
To bake the tofu, preheat the oven to 425 F. Line a baking tray with parchment paper and add the tofu in a single layer so they don't touch.
Bake the tofu for 15 minutes. Flip each piece, adding more marinade over the top. Bake another 5-10 minutes until the slices are brown and firm.
While the tofu bakes, cook the noodles according to the package directions. Rinse the noodles in cold water after they are done to keep them from clumping.
Add the noodles to 2-3 bowls and mix them with half the remaining dressing.
Add the tofu slices, cucumbers, radishes, scallions, and chopped cilantro if using.
Spoon over the rest of the dressing or serve it at the table. Serve the bowls with lime wedges.