Preheat oven to 425 degrees F and line a sheet tray with a wire rack.
Place the baguette slices on the rack. Brush both side of the slices with 1/4 cup olive oil and sprinkle with salt and pepper. Toast in the oven until light brown and crispy, about 6 minutes. Let cool, then rub each slice with the whole clove of garlic.
Heat the remaining 3 tablespoons olive oil in a large fry pan over medium heat. Add minced garlic, crushed red pepper and thyme and cook for 1 minute. Add grapes and olives and cook, stirring, until heated through and grapes begin to soften, 3 to 4 minutes.
Spread about 1 tablespoon goat cheese on each crostini. Top each with the grape and olive mixture. Transfer to serving platter and serve.