Sort your data out before you leave. Buy your plan online, and you get a QR code by email. Scan it while you are still on your home wifi. Your phone saves the eSIM but does not start the clock yet. The plan only begins counting once you land and turn on data in the Faroes.
Check your phone first. An eSIM needs an iPhone 11 or newer, or an Android phone from around 2020 onward, and the phone must be carrier unlocked. If you are not sure, search your settings for the word eSIM. If it shows up, you are fine.
Doing this at home means you skip the airport SIM kiosk and the queue. You also avoid paying roaming fees the second your plane touches down.