[Subscription/Change] Do you have any services that I can sign up for by using a passport, such as a prepaid SIM card, before an Alien Registration Card(ARC) is issued?

You can purchase data and voice services from 5 to 60 days from the following: https://roaming.lguplus.com. (Korean, English, Chinese, and Japanese available)
You can purchase a USIM and eSIM, or rent a Wi-Fi router and mobile phone.
For an eSIM, you can purchase and register it on the website above without going to the airport.

[Buy USIM or eSIM]
Call from Korea: 010-3998-1004
Call from abroad: +82-10-3998-1004
Messenger ID: lgcscenter (Kakao Talk/WeChat/Line)
Airport: LG U+ counter at Incheon/Gimpo/Gimhae International Airport