Trim excess fat from the pork shoulder and season all sides with sea salt, black pepper, ground cumin, and dried oregano.
Place the seasoned pork into a slow cooker and add the minced garlic, orange juice, and lime juice.
Cover and cook on low for 8 hours or until the meat is tender and easily shreds with a fork.
Remove the pork from the slow cooker, shred it using two forks, and spread it in an even layer on a baking sheet.
Drizzle a few tablespoons of the remaining cooking liquid over the shredded pork and broil for 3-5 minutes until the edges are golden and crispy.
Warm the corn tortillas in a dry skillet over medium heat until soft and pliable.
Divide the crispy pork between the tortillas and top with diced white onion and freshly chopped cilantro.
Serve immediately with a fresh lime wedge on the side for a bright, citrusy finish.