is it too soon?

Im 19 and very very shy. There is this girl in my class who also goes to a club on campus with me. She is so cute and nice and i forced myself to talk to her due ti my interest. We have talked probablly 5-6 times for a few minutes each time the past few weeks. She does most of the talking but ive started to try and say more though and its not that bad actually. I really like her and i want to give it a shot for once. Is it too early? I dont want to seem like a creep but i also dont want to wait too long and for anything that could have been to fizzle out. She seems generally friendly with me and always smiles when we talk and she even approached me in the campus dining hall earlier and asked how i was doing on an assignment.

when is the best time to do this and what is a good place for a first date i should suggest? I feel like if i ask her out at the begining of class and she says no it will make her feel awakward and trapped but if i ask after class ill have to wait for her to leave and that feels stalkerish (maybe not, idk as ive never done this before). I have her on discord and we have talked on there. Youre not supposed to ask people out over social media/text though are you?