Don't overthink it, just do it! One of my biggest regrets from college was when a girl who worked in the dining commons sat down to dinner next to me, but I just panicked and left. If she always eats alone, you must have a few things in common: hell, you may eventually even learn she's on the spectrum.
If you're nervous from overthinking this...um...well...just tell yourself "this won't translate into a 'date'", and whatever happens will meet or exceed your expectations, I guess.
No, I'm not being sarcastic. I just have no idea what I'm talking about. Just trying to steer you off my path, which led to a botched castration attempt right after graduation. With incelness, THERE ARE ALSO REGRETS!
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No one in the world ever gets what they want,
and that is beautiful.
Everybody dies frustrated and sad,
and that is beautiful.
-TMBG