6 AM flight out of Berlin airport BE, how early to leave?

I have a flight out of Berlin airport at terminal one to Amsterdam on Tuesday at 6 AM. I am staying at the Hilton in downtown Berlin. What is the best way to get to the airport at that time? Assume I need to arrive at at least two hours early? Is it better/ less stressful to arrive three hours ahead?
I was looking at public transport and it takes at least an hour to get there assuming all the connections and everything work. Would I need to leave the hotel and what’s the best rounding?
I did notice that some of the public transport seems not to run super early in the morning/late late at night.
Any suggestions are appreciated!