Absolutely. She's waiting for you to make a move.
If your class is right by lunch or dinner time (assuming you're in college based on your age) see if you can go get something to eat together on campus (or off campus but it'd probably be weird to get in a car together this early).
This'll give you a good opportunity to talk more in a really casual setting. Try to broaden more from class and school as the time together passes.
If you're not by a food time or just have classes soon after that, see if you can meet up about your class you share. Ask her to dinner and then a study session at the school library or whatever. Anything to get some time alone with (at least) a portion of the time not dedicated to the class.
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