For a private, most of the time I have a pretty good idea what the student is interested in by the end of the lift ride. Many times, just watching two turns is enough to know where to start teaching. Sometimes I'll need to see more turns, but since I only have an hour, it does not make sense to me to use a whole lift ride to make an evaluation that I can usually make in a few seconds. If you've told me what you want to learn and I can see something that's a good fit right away, it's time to get started. We can always "course correct" in the middle of the lesson if we need to.
For me, teaching a student for the first time is kind of like how a travelling chef deals with a "cook this" challenge. Even though every kitchen is different and the ingredients may vary, the chef knows what kind of pans to use for different dishes, has a personal bag of tricks with spices and flavorings, can recognize big trouble ahead of time and will make adjustments for things like altitude, the local flavors of the ingredients and the personal tastes of the diners. He learns to make plans quickly and deal with the surprises as they arise. Each dish that results may be unique, but the mechanics of the underlying process varies little from dish to dish.
In reality, I never start teaching "right away", but sometimes it may seem so. For example, if I have a level 2 student, one of my first questions is "Do you have trouble getting off the lift?". If the answer is yes, we'll go over some stuff/do some drills before we get on the lift. For a first time skier in a private, I use the transit time between the private desk and the lesson area to gather info that I can use to modify the basic lesson format (e.g. balance while walking in ski boots can tell me whether or not the student can go direct to parallel). The first time student may think I start teaching right away, but I've already eyeballed their clothing and equipment, made an assessment of their psychological state, tried to suss out their preferred learning style, probed for other sports they do and made plan adjustments before we get started. But I do these things for all students and that's really part of what teaching is all about. So, in reality, I always start teaching right away
! That is what you paid for, isn't it? Or did you just want to cut the lines?