How long to clear immigration arriving in Athens?

Impossible to predict with any degree of accuracy. Will your flight be on time? How many other international flights will arrive at or shortly before yours?. Will all kiosks and/or desks be open? Will you also have to wait for checked bags? Could be 30 min. Could be an hour. Could be more. Maybe play it safe and ask for a time an hour after ETA, which would give a 2 hr window.

Athens Airport Taxi Fares
Athens airport taxis offer a set fare for the journey from Athens Αirport to the center of Athens. Thus, during the day shift (05:00 am – 00:00 am), the taxi ride will cost you 40€/42$, while during the nighttime, the price rises to 55€/58$.
https://athens-international-airport.com/airport-taxi/

Maybe just get a taxi at the official taxi line when you are set to go?

As Joe said, if you're worried about potential delays, take a taxi without pre-booking.

The official fare is actually €40 during the day / €55 from midnight to 5 a.m., as indicated on the sign in front of the taxi rank.
See below:

https://photos.app.goo.gl/EVNQHn9UZrRL6S3v9

Metro and buses also available at the airport don't need to be pre-booked.

Agree with Joe & Jo-lui ... and would just add this. Very occasionally a "rogue" taxi driver, when you arrrive at your place, may try to add to official fare (claiming bag fee etc) ... a precaution, simply use phone to take photo of rate sign..

After taking photo of sign. Let the taxi driver know you are fully aware of the cost and that there are no extra charges for tolls etc.
Also double check that your destination is in the flat rate zone.
Do this before you get into the taxi.

Now I am confused. Having seen multiple recommendations here for Welcome Pickup in Athens, we had planned to use that service to pick up several family groups on arrival for transport to our Athens hotel. Yes? Or, no and use taxis instead? Please advise.

Thanks for the advice. I was planning to book the pickup because I have heard that many taxi drivers try to charge more than the fixed rate, and I don’t want to be fighting with the driver after a very long flight from the US.

If that isn’t likely to be a problem, especially with the suggestion of taking a picture of the rate card, then just grabbing a taxi on arrival is certainly easier.
I’m staying by Syntagma Square, which I believe is comfortably within the 40e zone.

Everything is explained on the Welcome Pickups website:

https://support.welcomepickups.com/en/articles/4698590-how-long-will-my-driver-wait-for-me

Calculate an average estimated time when you think you'll meet the driver, taking into account delays due to passport control, baggage claim, etc. Just like a train won't wait for you if you don't show up at the platform, a pre-booked taxi can't wait for hours for free.

To get to Syntagma Square, you can also take the X95 bus (exit 5, arrivals level) for €5.50 or the metro for €9. You don't need to buy a ticket; a contactless Visa or Mastercard credit card can be used to validate your trip.

As expat-nomad said, with an unbooked taxi driver, before he puts your luggage in the trunk, let him know you're aware of the fare. No haggling, no negotiating, no extra charges. End of story.

We’ve been through immigration at Athens airport three times and each time we breezed through it effortlessly. The first time we arrived around 9 am. We took the metro to monastiraki and our hotel. The second time we arrived at 5 pm and while it took us a little longer we were outside on the metro platform around 48 minutes after disembarking. The third time we arrived around noon, and yes, while it was much busier overall due to the time of day, we still didn’t have any issues going through immigration. It did take about 38 minutes (yes, I time and save these pieces of data because my OCD requires it). Anyway, again, the third time, we were on the platform of the metro one hour and 15 minutes after disembarking. That time it took the train longer to arrive than it took to get through immigration and all of us on the platform, except for the airport workers heading home for lunch agreed about that. We always take the metro in Athens as it’s quite convenient. We also use it to get to Piraeus for ferries.