This question really brings back memory.
I remember playing a game, some kind of dancing game and SNSD's songs were there. If I recall correctly their first song I listened to is Genie, Gee, ITNW era. Their dance is so iconic and covered by a lot of boybands groups and I think that's what made me search their name in YouTube. Genie, both the dance and the song (TaeYeon's high note <3) instantly hooked me up, and I've been following them since. Although I'm mostly into boy-group, SNSD is one of a few exception. Love them.