This. Precisely this. I would just like to add that the lean in does work, but only when its pretty clear that you're having a great time and are very comfortable with each other. e.g. holding hands in a booth in a bar, dancing together and having fun etc.
But there are also many women, in my experience, that for whatever reason, don't or can't signal their interest or intentions. In that case I ASK them. It sounds very awkward to say it, but if done in private (i.e. you don't shout it out) I've actually noticed it creates a lot of comfort in the women. e.g. once I asked a girl I was on a date with, and she said she wasn't comfortable with PDA (we were inside a bar). I didn't push it, but after we left the bar and nobody was in sight outside, we did make out. I like to think if I had just "gone for it" in the bar, she would have been uncomfortable, I would feel rejected, and generally bad things all around...