What would be the best option for transport of 4 adults and luggage at this hour?
Your hotel can probably arrange a taxi.
The good news is that traffic should be light………
Our hotel in Ljubljana arranged a taxi for us in an almost identical situation 2 years ago. Even though the hotel was in a pedestrian zone, the taxi was able to come to the front door at that time of day.
I had a 6am flight last Tuesday. Hotel got me a taxi. I was there at 5am. Just me, myself and I. Airport opens at 5am so the 2-3 hours ahead just doesn't work.
I had that situation for my RS Adriatic tour in 2023. Another couple also had a very early flight, so we shared the taxi. We arrived at the airport before we could move into the next section within the airport.
The airport isn’t very close to the city but most of the drive is freeway. Should take about 30 minutes. So probably ask your hotel the night before for a taxi at 4:30, but they will have done this thousands of times and can recommend the best time.