This is just to clarify, but a K close means you kiss her. It's short for kiss close. Your thinking of an F-close, which stands for F@ck close or full close, depending on who you ask. That's when you have sex with them.
Honestly, I have no earthly idea. I get what you're asking, and I wish I could help, but I have no idea how you'd pick up a girl without picking her up. You'd need to talk to someone who's very knowledgeable on the subject of indirect daygame (which is very rare. day game normally requires you to take the direct approach)
Shot in the dark, but I'd say start off a friendly conversation, tease her a little bit, little bit of flirting, then N close (Number Close). Then you could ask her out and it's business as usual