As OP said, the typical way to go into management consulting or investment banking or another of these "big bucks" careers is to do it right from the start. Going to a "prestigious" undergrad school helps immensely. Being able to look and talk like a big shot helps. Slog it out in a bank as an analyst for some years. Then at some point go to MBA school as a finishing degree, and then back into a bank/consulting company as a made man higher-level employee. The key is to get that "elite" pedigree early, which opens the rest of the doors.

There are also career changers who start out as something else (like a software developer) and go to the best MBA school they can get into, in order to try to "sneak in to the back door of the club" that way. I actually tried (and failed) to walk this path. My jaded view, after blowing more $ than I care to admit on B-school and literally dozens of interviews that went nowhere, is that these employers are looking for people already in the in-crowd, pre-blessed as elite, and are in general not welcoming to working class career changers. Investment banks are primarily looking for pedigreed former bankers, and management consulting firms are primarily looking for pedigreed former management consultants, and good luck if you're not already in one of those clubs.