Begin by making the syrup: add berries, thyme, water, and sugar to a saucepan and bring to a boil.
Reduce heat to a simmer and use a wooden spoon or fork to break down the blackberries. Once they're mostly broken down, pour mixture through a strainer and into a pitcher, using a spatula to press mixture through the strainer more quickly.
Next, add tequila, triple sec and lime juice to the same pitcher and stir. Top the pitcher off with sparkling water.
Adjust to taste--either add more tequila and/or blackberry syrup and enjoy!