Preheat the oven to 350°F (175°C) and spread about 1 cup of salsa evenly over the bottom of a 9×13-inch baking dish.
Bring a large pot of salted water to a boil. Add the jumbo shells and cook 8–9 minutes, just under al dente so they are flexible but not floppy. Drain in a colander and set aside to cool slightly.
Heat the olive oil in a large skillet over medium-high heat. Add the minced garlic and cook 1–2 minutes until fragrant.
Add the ground beef to the skillet, break it up with a spatula, sprinkle with 1/2 teaspoon salt, and cook until no longer pink. Drain excess grease if needed.
Stir in the corn, taco seasoning, and 1/4 cup of the salsa. Cook until heated through and the seasoning is dissolved.
Remove the skillet from heat and stir in 1/2 cup (about) of the shredded cheddar until just melted; this is the filling.
Fill each cooked shell with an even amount of the beef-and-cheese mixture and arrange the shells in rows on top of the salsa in the prepared baking dish.
Drop the remaining salsa in spoonfuls over the tops of the stuffed shells, then sprinkle the remaining shredded cheddar evenly over everything. Cover the dish with aluminum foil.
Bake for 20–25 minutes, until heated through and the cheese is gooey. Remove foil for the last few minutes if you want the cheese more browned. Serve warm.