advice on getting internship?

I am a sophomore international student (I am not familiar with the system here but I think freshman with 30 credits transferred from exams are considered as sophomore?) from a semi-target/non-target west coast business school. My long term goal would be getting a law degree and land a job in legal sector in my home country (in Asia).
I have no connection, no impressive activity (the best one I can think of right now is a summer course in accounting/finance). I want to do an internship that can make my resume looks better or increase my chance of getting a decent job in finance in case I cant get into T14 (or makes my resume looks better when searching for an internship after I get into T14). Anything in finance/auditing/regulatory is fine.

I found that most internships are only available for penultimate students. I can apply even I am not but I am afraid that my profile is not strong enough for them to take a non-penultimate student. Is cold-emailing effective for me given my profile right now is not really impressive? Is it true that many firms are not willing to take interns as dealing with a kid who knows nothing in "real world" finance is a waste of time and they would not consider a person without family connection because he could not bring deals for the firm?

Thanks a lot