Preheat oven to 425°F Unfold puff pastry and cut a 10-inch disc. Cover and keep refrigerated.
Melt butter in a large skillet over medium heat. Add onions and a pinch of sugar and cook, stirring, until onions are golden and caramelized, about 15 to 20 minutes. Add 2 tablespoons of water to deglaze pan, scraping brown bits from bottom of pan. Transfer to a bowl and reserve.
In a clean, oven-proof 9-inch skillet, combine 1/4 cup sugar and 3 tablespoons of water. Cook over medium heat, swirling gently (do not stir with a spoon) until sugar melts and turns into an amber-colored caramel, about 5 to 7 minutes. Add vinegar carefully and swirl again. The caramel will seize, but will re-melt in the oven.
Sprinkle olives over caramel, then scatter tomatoes over olives. Sprinkle onions on top, then season with thyme, salt and pepper. Top with puff pastry circle, tucking edges into sides of pan. Cut several vents in top of pastry.
Bake until tart crust is puffed and golden, about 30 minutes. Let stand for 5 minutes, then run a knife around pastry to loosen it from pan. Flip tart onto a pan lid and slide onto a serving platter. Cut into wedges and serve immediately.