Read job posts of US government positions related to Korea. They require fluent Korean. Intermediate level won't cut it.

Also, there are over a million Korean Americans in the US. Many are native fluent in Korean.

That hiring manager in the US won't be impressed you went to a Korean university they never heard of before. A lot of overachieving Korean Americans going to Ivy League or UC Berkeley is going to apply for those same jobs. They've also lived or been to Korea. What do you bring to the table?

I spent 10 years in Korea, even getting my MBA in Korea. I work in the government now, but not in a role that had anything to do with Korea. My Korean is Advanced but not fluent enough. Any US government job related to Korea would require you to process information from Korean sources and report or translate into English.

Go to USAjobs site and search for Korea related jobs. Read the job descriptions and see if intermediate Korean would get it done.