In a blender or large food processor, combine the olive oil, onion, garlic, cilantro, salt, cumin, oregano, paprika, pepper, and achiote paste. Blend, adding the orange juice and lime juice until everything is combined. Set aside ¼ of the marinade for later and transfer the remaining ¾ of the marinade to a large resealable ziploc bag or shallow dish.
⅓ cup olive oil, 6 cloves garlic, 2 teaspoons ground cumin, 2 teaspoons kosher salt, 1 teaspoon freshly ground black pepper, 2 teaspoons Mexican oregano, 2 ounces achiote paste, ½ cup fresh orange juice, ¼ cup fresh lime juice, ¼ white onion, 1 teaspoon smoked paprika, ½ bunch cilantro