Begin by preparing the vegetables. Thinly slice the cabbage and bell pepper into fine strips. Shred the carrots using a grater or food processor. Place all the vegetables into a large mixing bowl and toss thoroughly to combine and evenly distribute the colors and textures.

Transfer the mixed vegetables into a clean glass jar, packing the mixture tightly to make room for the marinade and to ensure full immersion.

In a small saucepan, combine the water, sugar, and salt. Bring to a gentle boil over medium heat, stirring occasionally to dissolve the solids completely. Once the mixture reaches a boil, remove it from the heat. Immediately stir in the distilled white vinegar and olive oil to complete the pickling brine.

Carefully pour the warm marinade over the cabbage mixture in the jar. Use a spoon to press the vegetables down, ensuring they’re fully submerged.

Let the jar cool to room temperature before sealing with a lid. Refrigerate for at least 12 hours to allow the flavors to develop. Serve chilled as a vibrant side or condiment.