Heat the oil in a large nonstick frying pan over medium heat until shimmering. Meanwhile, pat the fish dry with paper towels. Sprinkle evenly with the cumin, salt, and pepper on both sides. Place the fish in the pan and sear undisturbed for 1 minute. Carefully flip with a flat spatula and sear for 1 minute more. Transfer to a plate and set aside (the fish will not be cooked through at this point).
Add the garlic to the pan. Cook, stirring occasionally, until fragrant, about 1 minute. Add the vinegar and use a wooden spoon to scrape any browned bits from the bottom of the pan. Stir in the salsa.
Return the cod fillets and any accumulated juices to the pan. Simmer uncovered until the fish is opaque and just cooked through, 2 to 3 minutes.
If using rice, place in 4 shallow bowls. Place a piece of fish in each bowl and spoon the salsa around it. Sprinkle with the oregano and serve immediately.