alt Hacker NewsIs there a fourth way of doing it by befriending a random person who already works there and can get shoehorned in? Probably not, I'm sure they care about the pedigree more than basically anything else.
I send an application to RenTec every six months, almost as a joke because I would be extremely surprised if they continue after seeing <NOT A TOP 20 SCHOOL> on my resume. Granted, I don't think you really "apply" to RenTec to begin with, I think realistically they actually find you.
Yes, if you know someone and they can vouch for you and provide an introduction, that's a possibility, but you will need to have some prior experience that's relevant to the role.
The other way would be to be working at a management or strategy/IT consultancy that is working with the financial institution. That way you can build your own relationships, understand their business and get head-hunted into an internal role when one comes up.