Combine sugar and vinegar in a small saucepan. Cook over medium heat, stirring, until the sugar dissolves and the mixture looks slightly syrupy, about 3 minutes. Remove from heat and let cool.
Cut off and discard cucumber ends; cut the cucumbers in half crosswise. Cut each chunk in half lengthwise. Smash each section with the side of a cleaver or chef’s knife. Cut each smashed piece crosswise into ½- to 1-inch pieces.
Place the cucumbers in a medium bowl; sprinkle with kosher salt, tossing gently to distribute the salt. Let stand for 15 minutes.
Drain the excess water from the cucumbers, pressing lightly with your hands to strain as much liquid as possible without crushing them. Dress the cucumbers with the vinegar-sugar mixture. Add garlic and sea salt; toss lightly.
