I wouldn’t say it comes from Korean, more like it and its analog in Korean probably have a shared origin due to the mixing of ancient Koreanic and Japonic peoples pre-migration and during migration. It may have come from a different language that doesn’t exist today, it may have originated in proto-Korean or proto-Japanese, or Koreanic and Japonic language speakers may have just changed each others language in a way which caused the particle to emerge in both languages (which is certainly plausible given how much they influenced each other’s grammar in general).