use a negative as positive. go up to her and say :"hey I noticed you look like you are having a bad day, let me make it better by buying you a cup of coffee, etc"
that right there, evens the playing field instantly. In 2 senctences you have 1. acknowledge that she looks like a **** and that you notice that she is trying to ward you off with her look, 2. bypassed that like a real man should and 3. becuase you have stated the unspoken rule, that you aren't supposed to call me out on that type o stuff, she is defenseless. what is she going to say lol, i was looking at you like that so you wouldn't approach me. the day a woman has the balls to say that I will give up lol. it won't happen. she will make up some BS excuse but the ***** shield would be taken down.
you have to look at approaching women from an offensive standpoint instead of a defensive standpoint. too many guys cherry pick women that look all too easy, and are to reaction based in their approached. Take what the defense gives you when it comes to approaching. Attack the woman (not physically lol), put her on the defensive. Instead of thinking wow should I approach her, you should be thinking "dman that's an IN right there, she is giving me something to work with"
Every approach while different, is the same. The first thing you have to do, is establish frame, and do so quickly. Within a few seconds, you have to establish that you are on the offensive and she is on the defensive. You can't get a woman while playing defense which is what too many guys do "hey, i'm presenting myself, please don't reject me, please, pretty please, you are cute, oh.. yeah i know i'm not supposed to be talking to you please forgive me, okay i'm leaving now lol". When I do/did approach women, I generally just got to the ****ing point and worked from there. My fiancee and I had been eye ****ing each other for like a week before I approached her, so I said look, I have seen you looking at me and I have been looking at you, let's cut the **** and do lunch, give me your number. Then you just work off that. You see a girl, think of what you want the outcome to be (within reason lol), and go with that. Be as direct as you possibly can. "hey, I want you to give me your phone nmber and I'm going to take you out tomorrow night". Bam, direct, to the point, there is no beating around the bush with what you want, that type of behavior nips friend zone in hte ass instantly. She either is or she isn't., MOre than likely she will be taken back by your bluntness and you an work from there, but the frame of the conversation is established. You aren't like most guys who come and flirt and beat around the bush with what they want when it's all so ovbious. She most likely will say something like "I just met you! or "i don't know your name!" or "wow that's blunt are you always like that" (when i see something I want yes, and I want you while looking directly into her eyes is the correct answer here

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What I have also found, it's the equivalent to a trick play in football. You don't give the defense time to prepare for it. All guys are all too ovbious, going to the cashier like 5 times and talking about BS and the girl is like "okay, the guy is going to ask me out sooner or later, how can i reject himm..yes i'm going to go with the I have a boyfriend route yes that's a good option"... but when you are that blunt, that quick, she doesn't know what hit them, they will say the first thing that comes to mind. if a woman tells me she has a BF in that instance, she usually does and she likes him becuase that was instinctive. I don't press at that point.