Season the trimmed pork shoulder evenly with sea salt, black pepper, ground cumin, and dried oregano.
Place the seasoned pork into a slow cooker and add the minced garlic and orange juice to the pot.
Cover and cook on low for 7 to 8 hours (or high for 4 hours) until the meat is tender enough to shred easily with a fork.
Preheat your oven broiler to high and line a rimmed baking sheet with parchment paper.
Remove the pork from the slow cooker, shred it with two forks, and spread it in a single layer on the prepared baking sheet.
Drizzle a small amount of the cooking liquid over the meat and broil for 3 to 5 minutes until the tips of the pork are golden and crispy.
Warm the corn tortillas in a dry skillet over medium heat for 30 seconds per side until soft and pliable.
Assemble the tacos by dividing the crispy pork between the tortillas and topping with diced red onion, fresh cilantro, salsa verde, and a squeeze of lime.