Less than a minute at GIB, before I became a British citizen.
Everyone else was in the British/EU/EEA queue, so I went straight to the front of the non-EU queue after a few seconds walking off the flight to the immigration checkpoint (there are no airbridges and there's usually only one flight arriving at a time), "how long are you staying?" "1 day" stamp! Then a few seconds to walk out of the terminal.
While Greenland is not part of the Schengen area, it is part of the Nordic Passport Union and in any case flights from the Schengen area generally do not go through border control.
https://naalakkersuisut.gl//en/About...n-and-Tourists
Greenland is not part of the Nordic Passport Union, despite it’s current affiliation with Denmark. Norway’s Svalbard is also not included in the Nordic Passport Union, IIRC.
The fastest processing time involving passport control for me has taken place before I could even get off the planes. But for more common experiences of fast processing during commercially scheduled travel on common carriers, I’ve had many times where I encountered no passport control line and the passport control authorities just looked at my passport cover or bio data lags and let me through in 30 second or less. And yet at other times these same ports of entry have had me seeing lines taking 40-200+ minutes.