A few hours ahead, prepare 2¼ cups drinking water. Keep it in the fridge until cold.
In a blender, add ¾ cup cold drinking water (the prepared one), mango cubes, and sugar. Blend until smooth. Pour through a fine mesh strainer into a measuring cup. Discard any fruit fiber. Cover the mango puree with plastic wrap and keep in the fridge until ready to use.
In a medium bowl or measuring cup, add matcha and ¼ cup hot water (175˚F / 80˚C). Whisk until matcha is blended with no lump. While whisking, slowly pour in 1½ cups cold drinking water.
Prepare 2 large serving glasses. Add ½ cup of mango puree into each glass. Top each glass with 5 ounces ice cubes. Give the matcha a quick whisk and divide into the glasses. Serve cold.