Recent Graduate trying to break into IB

I recently finished my undergrad after this past summer semester near the top of my class at a large non-target state school in the US. I was planning on going to Law school until my senior year, but after doing some research I am interested in the world of IB. I am definitely late trying to break into the Banking World - I didn't do any related internships or summer analyst programs. I have been working for a commercial real estate development company for the past 3 years and just came on full time as a data analyst. I am interested in being hired on as a full time IB analyst - particularly in Canada or New York. Does anyone have any advice on what I should do or where I should begin? Do I have any chance at blindy applying to a large bank or boutique firm?