Clean a 1-quart heatproof jar with hot, soapy water and rinse well.
Peel the red onion and cut into thin slices (about 1/8 inch). Pack the sliced onion into the jar, leaving 1/2 inch of headspace.
Combine the water, white vinegar, granulated sugar, and kosher salt in a small saucepan.
Bring to a simmer over medium heat, stirring until the sugar and salt dissolve, 2–3 minutes.
Pour the hot brine over the onions, pressing gently so the onions are fully submerged. If needed, stir to release air bubbles and top up with brine.
Let cool at room temperature until just warm and the onions turn bright pink and slightly tender, 20–30 minutes.
Seal the jar and refrigerate until crisp-tender and well flavored, at least 1 hour (best after 24 hours). Keep refrigerated and use within 2–3 weeks.