As others have said, Chinese Characters passed through Korea to Japan by the 3rd century CE. IIRC the Japanese actually have a named mythological/legendary Korean dude who brought it over.

Hangul wasn't until the mid 15th century, and even then it was quickly repressed by the aristocracy/noble classes who continued to write in Hanmun, Chinese Classical writing style. Hangul didn't really become widespread in use until the very end of the 19th century in patriot literature. In any case, the Japanese had their our writing, a syllabulary(?), by the 9th or 10th century, in hiragana and katakana.