When meeting someone for the first few times, do you necessarily show your interest openly right away?

Anonymous
There's this guy I've met through mutual friends twice, and I get the vibe that he's interested in me, since he looks at me a lot and acts kind of nervous. But it's only a vibe I get. He hasn't asked for my number or anything - is it safe to say if he were really interested he would've asked by now? Or at least asked our mutual friends for more info about me? I find it hard to believe that anyone is THAT shy.
When meeting someone for the first few times, do you necessarily show your interest openly right away?
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