early morning transport to Geneva Airport

Is this the Holiday Inn you are staying in?:

https://www.ihg.com/holidayinnexpress/hotels/us/en/geneva/gvarp/hoteldetail

If so you can take the bus; there are 3 of them that stop at the bus stop near the Holiday Inn Express; it is free the hotel will give you a pass. There is no subway in Geneva. There are only trams and buses

Subway

Blandonnet
2 minutes walking distance in direction of the airport
Estimated distance to the hotel: 0.31 MI/ 0.5 KM
Cost of Underground: free of charge for hotel guests

https://www.ihg.com/holidayinnexpress/hotels/gb/en/geneva/gvarp/hoteldetail/directions

No personal info, but it appears the hotel staff should have the answer/directions for you

It looks to be a local transit station.

Check the map here.

https://www.tpg.ch/sites/default/files/2021-06/plan%20multimodal-tpg-h20210704triforcev8.pdf

And a station overview here.

https://www.tpg.ch/sites/default/files/arretsplandeconnexion/BLDO12122021.pdf

Please do check that those are the official sources for transit info in Geneva.

I used to live in Geneva, and I know of no subways (as we Americans think of them) in Geneva, other than the underground train that goes between the airport and the main train station at Gare Cornavin.

Sometimes Europeans refer to underground pedestrian tunnels as subways, and that is probably what they mean, since the Holiday Express I looked up is at the corner of the airport. It looks like a 10 min. walk to the airport entrance.

Yes, "subway" refers to a bus stop in what we Americans would call a "Highway underpass". Photo.
https://www.google.com/maps/@46.221986,6.0973347,3a,37.5y,293.46h,87.33t/data=!3m6!1e1!3m4!1srmHogfG-a53YbJD1YO07ew!2e0!7i13312!8i6656

Google maps shows it to be about 700 ft from the Holiday Inn Express walking away from the direction to the terminal.

Thank you, everyone for your responses. Now I know what a "subway" means in
Switzerland and I think I can find my way to my plane! Thanks again.