Get to Florence airport?

Taxi
It’s about a 15-20 min ride

I believe the fixed rate is 30 euros, might be a bit more at that hour

What time is your flight?
Since it is not going to US arriving 1.5- 2 hours in advance is sufficient
You might check with airlines and ask what time check in desk opens

( there are no direct to US flights out of Florence and the tram begins running at 5 am)

Taxi being the easiest way, it is better to reserve the day before. You could ask your hotel concierge or phone 055-4242 or 055-4390 or 055-4798. When they take the reservation, they are very reliable; a taxi will be waiting you at the agreed time and if you are more than two minutes late, the driver will phone to check.

Being at the airport 2 hours prior to departure is way more than you need. Florence has only regional flights on small regional jets (A319 and Embraer190). I think the airport opens its doors at 4 or 4:30, but you can’t check in more than 2 hours prior to departure.

Returning home from Florence on our early a.m. flight connecting through Amsterdam this past November 30, we were amazed at just how quickly we got to the airport from our short stay in the Santa Maria Novella neighborhood, arriving at 0:dark 30 in the morning. We were convinced that we were both there far too early and were going to be met with a deserted like space with no services open and available. Surprise, our gate area was absolutely jam packed, seemed crazily chaotic and definitely caused some initial concern. Happily our line moved with efficiency and for the 20 - 25 minutes we queued, the massive group was processed impressively quickly. Being met by a smiling, friendly agent at the counter who handled our bags swiftly like the pro she was, was an absolute delight. Then, grabbing a bite and espresso after, also amongst a large crowd of travelers, we were also in good hands since everyone behind the counter were equally on top of their game, super fast and expert in filling orders. What at first blush seemed to be a nightmare scenario needing to be endured ended up being the most pleasant airport experience I'd had in years.

Don’t get scared by the long lines at the desk if you arrive early. It is because a lot of people, especially international visitors, start lining up more than 2 hours prior to departure, so a long line forms as the agents for that flight don’t even show up but after 2 hours from departure. At first only one agent arrives, and after getting settled that only agent starts working. As the flight departure time approaches more agents arrive. By the time it is 1h prior to departure several agents are all hands on deck, and the line goes super fast. All the times I depart from FLR, I wonder why I didn’t arrive only one hour prior to departure, when the check in line is only 5 minutes.