Taxi very early am to airport in Rome

I've done it, its fine. You will want to arrange a cab ahead of time, I don't know if many are generally waiting at the stands at that time. Ask your airbnb owner or use a service like welcome pickups or rome cabs. Especially for 5 people - you will need 2 cabs or a van, probably.

4AM for a flight to another European country is fine. I don't think security opens until 3:30 or 4 anyway, so getting there earlier wouldn't be helpful. Look into that if you are concerned. A flight to the US/Canada would require more time, but I don't think any of those leave at 6:30.

Knowing where your departing flight lands would be helpful info, ( i.e., a Schengen destination or elsewhere?) as to how much time you need to build in for processing.

You can arrange a taxi the day before or call the same morning. They generally arrive within 5-10 min even that early in the morning.
If it's a Schengen destination, you are more than ok (with time to spare) to be at the check in counter 2 hours ahead of departure (4:30am).

Actually the flight is to SFO with a connection through CDG. Thx. And yes, leaves at 6:25 am, ugh.

Then it is a Schengen flight, since both Italy and France are part of the Schengen Area (basically equivalent to a domestic flight in the US). Two hours prior to departure are more than adequate. So you need a taxi to pick you up at Trastevere at about 4am.
You can download the ItTaxi App or call a taxi.
The number for the largest taxi company is +39063570
The second largest company is +39066645.
You can call ahead the night before or on the same morning. Generally they show up within 5 min.

Thanks to everyone for the information. I want to piggyback on the original query as I have a 6:30 flight to Amsterdam and then to Houston. Calling the cab a day before should work, correct? Also, is it safe to travel alone at that time?

Thanks to Roberto and to all who clarified this for me. Much appreciated, love this forum!

Yes, Rome is safe at night. Actually safer. Bad guys are still asleep at 4am.

Besides the ItTaxi app, you can book a taxi calling by phone (you can select the English speaking operator) or using the taxi companies websites.

For the largest company in Rome (actually in Italy), which uses the ItTaxi app, you can also open the site below, and click on "Taxi Click" icon. You can reserve a taxi that way.
https://www.3570.it/services

Thank you everyone for the information! I will also need a taxi to get from Airbnb to FCO for an early flight in a few weeks.

Knowing that Rome's FCO airport is (in my experience) one of the worst, most chaotic and disorganized airports in the world, maybe just stay up late and go there even earlier. (I truly hate FMO. Does it show?)

"FMO" is an airport in Germany https://www.fmo.de/en/

Our flight was at 10 am and we took a cab from Trastevere. I'd definitely try to book a cab the night before for your peace of mind. Especially, if you need a van. Its a fixed rate and the drive is fast. The concierge recommended getting there less than 1 and 1/2 hours in advance but we opted for two hours. You definitely don't need three hours. We were good but those were the show-your-COVID-test days and that was the biggest hold up. We were on American Airlines direct to Dallas (11 hours!) Everything went really smoothly. Have all your papers in line and your boarding passes available. Keep your passport out as you go through security because you will need it several times. I'm not sure if the international area of FCO is different but, except for the COVID thing, we found it easy and efficient to navigate.

Also, my sister and I felt really safe in Trastevere even when we were out kinda late at night. We liked the vibe there.

Curious as to when above poster has been thru FCO?
We’ve flown in and out if there twice in past 3 years and found it to be quick and efficient both ways
Really quick check in and super quick entry process both with checked luggage, once during all the extra COVID checks.

We spent almost three times as long getting thru the mess at Dulles on our arrival back to states
That was chaos and most likely where we unfortunately got infected with COVID

YMMV

A little late for OP maybe, but I wanted to add a quick on-the-ground report. Definitely book a cab ahead of time. We were in Rome last week, and 97% of the available rooms and apartments were booked. We tried to get a cab to a tour meeting place an hour early and ended up missing the tour as NO cabs were available at 2 or 3 different taxi stands and two taxi phone apps. Rome is heaving at the moment.

In addition to ittaxi, linked above, common phone apps include FreeNow and AppTaxi. AppTaxi is the one that we finally, finally got cabs through, but with six people we needed two cabs so that made matters worse.

Unless you book a van ahead of time, you will not be able to fit five people + luggage in one taxi. I used a car and driver service twice and found him very reliable - on time, big van, willing to manage all the luggage including my aunt’s walker. No connection, just satisfied customer. Centro Servizio Moretti

Hope this helps.

P.S. Confirm and re-confirm your lodging. Our VRBO host cancelled a reservation I had made six months earlier when we were only an hour outside of Rome, even though I had confirmed by phone the night before. Pretty sure someone offered him twice the price. It was a scramble to find anything, and we ended up staying outside of Rome for two of our four nights. I hope “revenge travel” settles down to a more sustainable pace soon!

We were last through FCO in 2015 and have avoided it since. If it has improved, that is great. Ultimately, back in 2015, despite arriving 3 hours before our flight, by the time we reached the counter the airline woman all but told one of us to start limping so that she could get us a way to speed things (those golf cart transports) up so that we could make our flight. It was insane. If things are improved, that is fabulous.

FCO is among our favorite airports. I have not experienced what the poster above commented on.

It has improved

Our departure in May 2022 we got out of the cab, checked bags, did all the COVID paperwork, passport check, got boarding passes, thru security etc and were at our gate in something like 30 min
This was a United flight that left 11ish, we arrived about 7:45 IIRC

Our arrival a few weeks earlier was just as quick- in a cab in well under an hour

I posted about it at the time.