Hey if you're casually chatting up girls without 'approaching' you're already doing it my guy.
Like 6 months back I had a girl from the past who popped back up and messed with my head, I quickly backed out of the conversation and needed a distraction afterwards. It was a weekday afternoon and I went for an aimless drive and ended up at a shopping district near my home. I went into several stores and was (subconsciously) compelled to talk to anyone I came across, mostly women though.
I went into Best Buy and chatted with a clerk at the cell phone desk, she was into me, but I wasn't into her and she was too old for me, but I still had a charming conversation with her. Practice! I then went to a sportings good store and was asked by a girl "If I needed anything" and I quickly took that prompt and turned it into a casual conversation, then flirting, then got her number.... and I did not approach.
Same day, Grabbed a coffee and went to a local river walk I frequent, parked myself on a bench with my bag and just sat there relaxing beside the walking path. Eventually I saw a familiar face, it was someone I went to highschool with. Her and I both had the awkward "hey you look familiar, do I know you"? and I invited her to sit and chat, we talked playfully for a good 30 minutes, got her number too.
You don't have to be 'on the prowl', although it has its merits. If you are warm and approachable and receptive to conversation you can take those interactions and transmute em into game. Every successful conversation is a win and moves you one step closer, either through practice or all the way to getting a number. I don't recommend being passive, but on the flip side I don't recommend super forward approaches in day game. Got to calibrate accordingly
