In this cases I usually book the night in which I will arrive as well and let them know, that I will arrive that early.
It happens occasionally with early or late - depending on your point of view) flight arrivals in Asia or the US. I arrived a couple of times around 01:30 am) and always had booked this night as well.
I do not want to argue with the night shift and just crash in a bed (which is confirmed for this night and not from 15:00)