Heat the milk in a small pot over medium heat until steaming with tiny bubbles at the edge and 150–160°F, 2–4 minutes; froth to fine microfoam if desired.
Place a fine-mesh tea strainer over a small bowl and sift in the matcha powder to remove any lumps.
Warm the water to about 175°F (just below a simmer; small wisps of steam, no bubbles), 1–2 minutes.
Add the granulated sugar to the sifted matcha, then pour in the hot water.
Whisk briskly in a back-and-forth M or W motion until the mixture is smooth, fully dissolved, and foamy on top, 15–30 seconds.
Pour the matcha base into a warmed mug. Slowly add the steamed milk, holding back foam with a spoon, then spoon a little foam on top.
Serve immediately while hot; the latte should be vibrant green, lightly sweet, and velvety.