Early Morning International flight from Venice Airport

You can't check in until the airport is open, but VCE-AMS is a "domestic" flight within the Schengen area, just like flying between US states, so you won't need as much lead time. With such an early departure I'd suggest staying at a hotel near the airport, preferably with a shuttle service. This one worked for me, there are others.

Venice to Amsterdam is NOT an international flight - it is within Europe. Be at the airport when it opens, you'll be fine. Just be sure the Vaporettos are running that early. If not, you'll have to arrange transportation. We do everything we can to never fly out of Venice because the flights are always so crazy early. It's always best to fly into Venice and out of another town when in Italy.

Just to continue the song. It is not an international flight. A standard domestic flight to your international flight. The Venice airport is pretty sleepy in the am. 4.30, 4.45 is more than enough time. You may be the only plane. This the main reason we constantly caution folks about flying home from Venice.

I might have described it incorrectly. I booked the ticket through Delta from Venice to US. It has a connecting flight from VCE - AMS-LA It just operates through KLM from Venice to AMS. I assume that I will have to go through the immigration there and the flight will be treated as international. If you have taken a similar trip - connecting fight in a european country before heading to US

Your passport processing, for your Schengen zone exit, will occur in Amsterdam.

Checking in at Venice will be like a US domestic flight.

Venice Italy to Amsterdam Netherlands is an international flight ( i.e., between nations) but the key factor is that it is an intra-Schengen flight so no passport control for that leg of your trip

"international" https://www.dictionary.com/browse/international

You described it correctly the first time. It is your understanding of the rules regarding intra and outside Schengen zones that is incorrect.

Regardless of who you bought the ticket from, your first flight, while technically international, is an intra Schengen flight. Thus it is treated as a domestic flight and there is no Passport Control. 2 hours before check in is all that is required. And you may well need to take a taxi from Piazzale Roma at that early hour of the morning if the airport buses haven't started running. The vaporettos should still be on their night schedule. Moving to an airport hotel the night before your flight makes a lot of sense.

You will go through exit Passport Control in Amsterdam. You will go through US immigration when you land at your US airport

We have stayed at the Marriott Courtyard, which is five minutes from the Venice airport, altho not walkable. I think the hotel has a shuttle, but you'll need to check the hours. Good luck!

"Does the airport really bot open until 4 AM?"

Yes.

Last year, I had a 6:40 am flight on Lufthansa. I arrived at the airport at 3:30 am, much to the amusement of my taxi driver who thought I was overly cautious. The lobby was nearly deserted, with only a few people trying to sleep on benches. Check-in for various airlines starts at 4:00 am, but Lufthansa's crew took 20 minutes to prepare before opening check in-lines.
FWIW, the Delta counter opened their check-in lines promptly at 4:00 am.

See https://www.veneziaairport.it/en/at-the-airport/airport-opening-hours.html
and also see FAQ https://www.veneziaairport.it/en/info-and-assistance/faq.html

"Access to the terminal is permitted from 4 a.m. The terminal closes with the last flight of the day, except for specific cases of prolonged airport activity."

Another way to look at it. You can book a ticket from Chicago to Amsterdam with a change of planes in New York where you board your international flight to Amsterdam.. Edit 1 -- Not till your feet are on US soil. Edit 2 -- Yes, no different than many airports in the US.

And to add a bit more to some of the confusion. Many check-in counters are not operated by individual airline but by private companies.

Just keep in mind that the desk for checking in may have combined Air France/KLM signage.