How do I transition from friendly hanging out to romantic dating?

Anonymous
So I guess usually I'm old fashioned and like to properly ask a girl out so we both know our intentions from the start but for a few reasons and circumstances I'm having to try something different.

There's this girl that I just met at of my weekly university events that I met and we got along quite well and exchanged all social media. We were talking about how there was other event, completely related to university, that she's interested in and I was going to already with my friends so I casually asked her to join me and my friends. I feel like if she joins me and my friends and we talk to each other and get to know each other then it won't be so sudden and random to ask her out on a date since we've already basically "hung out" casually.

So then after that when I see her at the university event next I plan to ask her out properly but without explicitly saying "I'd like to take you out on a DATE", keeping it a bit less formal. So for example if I asked her out for coffee, to dinner, to a movie, she'd get the idea that i's a romantic date that I'm after, right? I don't plan to do anything too romantic like a kiss or anything on this first date but I'll try all the nonchalant touching when I can. Then either at the end of the date or that night/next morning I'll ask her out on another date.

Now my question is, on this second date I want to speed up the pace and begin the proper romance. So how do I transition from friendly hanging out to romantic dating? I feel like randomly kissing her or being overly romantic like going for the hand hold way be too much, and just saying, "can we move this to romance now" isn't romantic. So how can I do it? And what's the best idea for each date? I was thinking a casual dinner at somewhere like a sushi bar is good because it's not too serious for "testing the waters" then for the second I would think maybe seeing a movie because that would be the easy way to test the romance and actually holding her hand would be more acceptable.
How do I transition from friendly hanging out to romantic dating?
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