In a small saucepan, set over medium heat, combine the cane sugar, water and thyme. Stir until the sugar has dissolved; bring to a simmer and then immediately turn off the heat, cover and allow to cool and steep, about 15 minutes.
Fill up four glasses with ice. Add an ounce (2 tablespoons) of syrup to each glass. Top with about 3 ounces of pomegranate juice and then top with the Truly Spiked & Sparkling Blood Orange. Give it a light mix and then garnish with thyme sprigs.