The Korean script is actually extremely simple. You could teach yourself to read it in just a few minutes. It won’t help you understand the meaning of the words, but you can at least know the sounds. Here’s a pretty good guide. Personally, having lived in Korea for a few years, I take issue with some of it. For example it’s generally more useful to think of ㄹ as L in all cases, not only when it’s a syllable coda, and some of the vowel sounds are especially poor (particularly ㅡ, which I think is better approximated for the average English speaker as a stronger version of the hidden vowel between the th and m in rhythm). But for the most part it’s very good.

But the main point is, even if you don’t learn to read the script properly, just spending a few minutes skimming through that guide should stick enough in your head to be able to easily and instantly recognise Korean as Korean.

The tricky one for me is Chinese and Japanese, if the Japanese text is heavy in kanji. Incidentally, Korean has its own equivalent of kanji. It’s called hanja (the regular Korean text is hangul). It used to be used in much the same way kanji is, but has largely died out over the last century or so.