Chopsticks entered Korea from China, as you seem to be aware of. They were already found in King Muryeong's tomb in the early sixth century, and they were common throughout the later years of the Three Kingdoms period, or the sixth and seventh centuries. This is in contrast to spoons, which existed in Korea at least as early as the Bronze Age.

But as can be seen in a picture of them, the Muryeong chopsticks were radically different from more recent chopsticks. This is because the chopstick underwent changes in shape (for instance, one side got thinner over time). Goryeo chopsticks from the 10th century.