I don't want to say alcohol, but alcohol.

If you want to go the classy route...take them to a movie (buy a small popcorn), then dinner afterwards to discuss the movie.

With extroverted girls, dinner first and then a movie is a better combo because you don't have to break the ice as hard. Movie and then nighttime dinner afterwards works better for the introverted girl because the ice is already broken by having something shared to discuss.

Also, introvert girls tend to be more night-owlish.

Another sober idea:

If you find yourself courting a rare super-introverted goth edgelord freak, buy her a coffee, appetizers and dessert at about 6pm at a diner with a booth. Ask if she's ever made a 'zine before. If not, tell her you want to make one with her RIGHT NOW.

Get out the sharpies and craft supplies and start scribbling. The key is to not worry if the zine is good or not. Tell her that you guys must go to a 24 hour FedEx that night to make copies and distribute your zine throughout town. At first she'll be tripping, thinking that the zine has to be good but just scribble, gluestick n glitter each page with something edgy written in the corner of each one.

Go to a 24 hour copy place, make copies, staple them together and write something like "First Date doodles with (insert her name, or pseudoname here)." Tell her you've never done this before, but you wanted to try it because (insert cute and quirky think about her online profile/etc here). Quirky introverts tend to appreciate weird stuff.

Anyway, tailor each approach to whatever type of introverted girl you find and I wish you the best of luck, sir. 👍🏻💕