Is a 7 am flight out of Zurich impossible?

There are multiple hotels INSIDE the Zurich airport.

Most of the airports in Europe have flights starting at 6:00 a.m. or thereabouts. In most cases, passengers will fly to a big city gateway airport where they'll sit around until mid-day or early afternoon. That's when most flights to North America leave.

Taking a 12 hour trip is tough enough. But getting 2-3 hours sleep and getting up at 3:30 a.m. to make it to an airport would push me past the point of no return.

When making reservations, we try to get flights out around 8:30a.m. or a little later.

Does this sound attractive?
https://community.ricksteves.com/travel-forum/switzerland-reviews/capsule-hotel-at-zurich-airport

The capsule hotel is not for kids.

Zurich is a very efficient airport, and you do not need to be there ages in advance. Where is the flight to?

When I had early flights I would stay at the Radisson. There are also two Hyatts, but I have not stayed there. In both cases you just have a short stroll to the departure area of the airport, so you can maximise your sleep.

`we have stayed at the Radisson Blu inside the airport terminal. The room was very nice with no noticible airport noise.

Wondering if a 7 am flight out of Zurich is a bad idea

If there is a later alternative, then my answer to the question you pose is 'yes'.

How 'bad' an idea it is depends on the age of the kid, to some extent.

Had a similar timed flight two years ago, and there were no security lines at six in the morning for our intra Schengen zone flight. Wife wanted to be two hours early and we compromised getting to the Zurich airport about one and a half hours before. Had plenty of time. But it was a flight within the Schengen zone, connecting flight to US was from Copenhagen.

Depends where you are flying to from Zurich. The further west in the US you go it may be a good idea to go early at 7am. Although some may disagree, the day before I fly home is a rest day. I do very little sightseeing, if any. I know that travel day is very long and tiring and I have ground transportation from my arrival airport as well. Kids generally sleep better than adults almost anywhere. It is you who will need the energy and patience on that travel day. Remember, "Early to bed, early to rise...it doesn't matter, you'll still be worn out when you get home!" :) Enjoy your trip.

My 3 or 4 time a year flight home from Budapest departs at 6:30 am. Taxi picks me up at 3:30 am. Been doing it for years. Layover at Frankfurt or Amsterdam is 2 to 4 hours and I am home early enough to do a few things and go to bed early. I sleep on the plane. But it's a preference thing.