When a person says "I would like to get to know you." What exactly do they mean? In my opinion, you can't really get to "know" anyone. Because to "know" something it takes looking at it from all angles, seeing it react in different situations and examine it inside and out. So, given this definition, does "I want to get to know you" mean that a person would like to look at the other from all angles? To see him/her react in different situations? To examine him/her inside & out? Of course, this can be done physically. Through sexual relations. But how would you go about knowing someone personally & mentally? You never know what they are thinking. This, in return, makes everyone become untrustworthy. Alas, to say "I would like to get to know you" means "I want to spend the rest of my life with you" ... Or does it?
Philosophers who talk about knowledge usually focus on knowing a fact ('knowing-that') or having an ability ('knowing-how'); but 'knowing-a-person' different from either of these types of knowledge. One one level, it is not very difficult: you could truthfully answer 'yes' to the question of whether you know Alexander George if you had say met him and had a few good conversations. And 'Know-who', as in 'Do you know who Alexander George is?' is even easier: you don't have even to have met him. At the other extreme, if 'getting to know Alexander George' required a kind of comprehensive knowledge-that of all the facts relating to him, you will never make it. Fortunately, you can make progress on getting t0 know someone without impossibly having the full story about them, if you can find out more about their personality and about what they think. And I am more optimistic about the possibility of that than you seem to be.