Flirting

What is the best way to meet a girl in a communal office space?

My company is in one of those WeWork's, and there's quite a few pretty ladies around that work in other companies on the floor or in the building. I am REALLY bad at this, and super afraid of rejection and awkwardness. I know I'll never be happy if I keep this attitude, but I don't know how to talk to them, and if they don't want to talk to me, etc... It's really hard for me.

The best thing I can think of is if they hold the door open for me I can be like "Thanks, by the way, I've seen you around, but we haven't met, I'm so and so" and then try to talk to them off of that. I dunno how I'd cold talk to them? MAybe if they sort of smile at me? But what if they don't look my way?
What is the best way to meet a girl in a communal office space?
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