As in Japan, Koreans first started writing with Chinese script, but Chinese script didn’t work well to write Korean for similar reasons that it didn’t work well for Japanese. (Japanese and Korean are syntactically very similar.)
One thing the Koreans tried was Idu script, a slightly modified form of Chinese characters. They took some of the Chinese characters and used them to represent meaning (which they would pronounce as the Korean word), used some other Chinese characters to represent sounds (which they would pronounce as the Chinese word), used a few other special symbols for grammatical inflections/declensions, and invented some characters (primarily for names). They generally used Korean word order.
This script was mostly used to help Koreans understand official government documents, which were written in Chinese with Chinese script.
CORRECTION: It appears that Idu actually came after Hyangchul. It’s a bit confusing because the term “Idu” is used both for a specific script used in 1390ish, and for the class of pre-Hangul scripts.