Cut the fish into 1-inch cubes and place in the freezer on a parchment-lined baking sheet for a few minutes until firm but not hard. Grind through the coarse disc of a meat grinder. (Alternatively, you can hand-chop the fish, which will take focus and perseverance, or you can chop it in small batches in a food processor, which will result in a slightly less-uniform grind.)
In a medium bowl, combine the fish, 1/3 cup lime juice, tomato, carrot and green chile. Cover and refrigerate for a few minutes for the flavors to mingle.
Taste and season with salt (usually about 1 teaspoon). Stir in a little more lime if the mixture looks dry or could use additional spark. Pile a portion onto each tostada and garnish with cilantro and avocado if you wish.