Mash garlic and salt into a paste with the side of a chef's knife. Transfer to a large shallow dish. Stir in 2 tablespoons molasses, 2 tablespoons lime juice, cumin and pepper to taste. Add pork and coat well. Cover and marinate in the refrigerator, turning occasionally, for at least 1 hour or overnight.
Preheat oven to 450 °F.
Whisk broth, remaining 1 1/2 tablespoons molasses, 1 1/2 tablespoons lime juice and oil in a 10-by-14-inch roasting pan. Add onions, sweet potatoes, okra and thyme; season with salt and pepper to taste and toss well. Cover tightly with foil.
Bake the vegetables until sweet potatoes begin to soften, 25 to 30 minutes.
Push the vegetables to sides of the pan. Place the pork in center and pour any remaining marinade over it. Roast, uncovered, until just a trace of pink remains in the center and an instant-read thermometer inserted in the thickest part registers 155 °F, 30 to 35 minutes. Transfer the pork to a cutting board and let rest for 5 minutes. Slice thinly on the diagonal. Serve with the vegetables.
Make Ahead Tip: The pork can be marinated overnight.
230 calories;7 g fat(2 g sat); 2 g fiber; 17 g carbohydrates; 25 g protein; 79 mcg folate; 74 mg cholesterol; 12 g sugars; 6 g added sugars; 195 IU vitamin A; 13 mg vitamin C; 89 mg calcium; 2 mg iron; 428 mg sodium; 819 mg potassium