How unbelievably corny would it be to give her a hand written letter?

From excrutiating experience, I cannot recommend this approach

I like this girl. She may like me back, Idk. But I'm head over heels for her, I can't stop thinking of her every day for the past few months. I wrote something for her on a notepad and want her to read it. Would it be cringe AF to put it in a letter, give it to her and ask her to read it when she gets home?

Hi there. Personally I think that's a lovely thing to do. It shows you have gone to some real effort, which I'm sure that she'll appreciate. Nobody takes the time to write letters these days, and so the fact you have made the effort will be special. I hope everything works out for you.