ok so when you first meet a girl, you are an unknown entity to them. They dont know anything about you, there is no past, she doesent know your bad habits, there has been no arguments or issues that you have to resolve. So this is an advantage and by virtue you are mysterious because of that and in a position to move fast.
Two questions......
1. How keep the mystery?
2. How do i move fast?

Maybe I am being Capt. Obvious but watch your social media settings and watch what Google brings up on you under your name. Two places you can lose the mystery real fast. My friend learned the hard way the other day he had a HB8 Google him with her smart phone. First thing it pulled up on him was his public arrest record. For whatever reason lol three public intoxication arrests didn't sit well with her.

Mystery is rather easy to keep.

Learn how to carry conversation based on the girl and environment completely, naturally, you'll reveal less about yourself.

When they ask probing questions such as your sexual history or if you're seeing any other women (depends entirely on how you feel directly lying to women), dance around the issue using sarcasm and playfulness. A joke remark diffuses some of the dangerous questions, and girls will often refrain from asking too many times.

Be naturally secretive. Don't reveal too much about yourself to anyone, let your actions do the talking. Example if you never talk yourself up or how good you are with women to your bros, yet they see you hooking up in the dance-floor, they can't help but think, how much of this aren't we seeing? I've built up an entire mysterious womanising reputation this way, my friends consider me a ladies man, yet i've never talked myself up in any way (bragging is BS). They've seen me do my thing, and it's what I don't tell, don't reveal, and don't deny that makes me mysterious.

Being mysterious also means refraining from verbally stating your feelings towards a girl. PUAs display this with kino and escalation. Never verbally revealing you like a girl is what keeps most girls guessing and unsure, (although to be honest, i've had flings and relationships flame out hard by abusing this.)

-SilverTonguedFox