Using a sharp knife or mandolin, carefully slice the cabbage into thin slices. The thinner the pieces of cabbage, the more quickly it marinates.
In a small pot, whisk together the vinegar, water, salt, and sugar over medium-high heat. Whisk until the sugar and salt are dissolved, just a few minutes.
Transfer the cabbage to a quart sized jar. Cover with the warm liquid, mustard seeds, and garlic clove. If the cabbage isn't fully covered, top off with vinegar or water, depending on how acidic you want the brine to taste.
Transfer to the fridge for at least 30 minutes. The liquid will be vivid pink when ready. The cabbage will be more tender but still have some crunch and bite to it, especially if the slices are thicker.
Keep refrigerated and enjoy within 2 weeks. Top off the pickling liquid with vinegar or water, as needed, to keep the cabbage fully submerged.