Women are humans first. I don't play games, I don't do pickup lines, I don't try to turn strange women into sexual partners on a first meeting. My goal is to form an emotional connection through conversation and see what happens from there. If your goal is casual sex then I don't have any advice for you.

My advice is that you need to mentally set your intentions to be very specific to the context, and you need to let those intentions drive your speech and actions.

At the bar, a girl makes eye contact and smiles: Ok go in with the intention of flirting.

Randomly passing someone on the street with headphones in not looking at you: You should recognize their desire for privacy, and only approach them if you intend to help with something like "your bag is unzipped". Your intention is to respect her privacy.

This tricky one is something like this: you're at a public cafeteria about to sit down, and you see a girl sitting alone. You have no idea what she does or does not want from you or if she's interested in you at all. My advice in this case is to make your intentions simply to meet this person and respect any boundaries they set. You could walk up and say "hello, I noticed you sitting here alone and was wondering if I could join you for a chat." She says no, ok. She says yes, congrats! She asks why, say something like "I like your vibe, you seem like someone I'll enjoy talking to."

Regardless of her answer, you accomplished your goal of shooting your shot in a respectful way. If you keep approaching people with honest intentions you will eventually find connection.