Is it a bad idea to cold email a hiring manager? Advice for non-target NE girl trying to break into asset management/commercial banking.

I’m a rising junior at a non-target-ish school in the Northeast, and I’m trying to break into asset management, ideally in Boston. I saw an internship I’m super interested in and was thinking about cold emailing the hiring manager to say I’m really interested and ask if I might be a good fit. Is that a dumb move? Or has anyone had success doing that? For context, I had a superday at JPM (didn’t get it), but the interviewers were actually really helpful and gave me great feedback for the future. That’s unrelated to this specific role, but figured I’d mention it since I’m trying to keep learning and growing from each experience. I’ve got a decent resume (solid experience, really good leadership, good GPA), but I know being from a non-target can make it harder. Any advice for standing out or breaking into finance/AM in Boston? Would also love to hear from any others who’ve done it from a similar background. Thanks in advance — appreciate any help or thoughts!