How to get a Korean phone number without an ARC?

Just arrived in Korea 3 days ago and I desperately need a Korean phone number. My ARC won't be ready for at least 2-3 weeks but I need a phone number NOW for KakaoTalk, Naver, and basically everything here.

I tried going to an SKT store but they said I need an ARC. Has anyone found a prepaid SIM that works with just a passport? I saw some SIM cards at the airport but wasn't sure if they'd work long-term.

Any recommendations? Budget isn't a huge concern, I just need something that works ASAP.