Something to keep in mind about your question is that the notion of college as a place to figure out what one wanted to be as an adult wouldn't become the norm until your grandchildren went off to college. Instead, you knew you were headed to a career in finance before you took one step onto your college campus and likely already knew the firm or office you'd be working with. I'll defer to those who know more about the history of employment in financial organizations, but from a higher education perspective, your path was pretty straight forward.
If you were a university student in NYC in the early 1920's, odds are you're white, male, and between the ages of 17 and 23. You likely attended a private high school or academy in the city and came from a family of means. Though it's possible you attended a public or charity school, you likely wouldn't have any idea what jobs in "high finance" were available to you if that were the case. Instead, if you had your eye on a job in a corner office (as it were), it's more likely you understood how Wall Street worked because your father worked for a firm and you made connections through his social or business network. What college you attended was likewise informed by your father's connections and social status.
If you were attending college in NYC, weren't Catholic, and came from a family with strong social connections, you were likely going to Columbia University, which meant odds are good your father did as well. In effect, you didn't have to go about getting the job - the job was yours the moment your father decided the job was yours.
If you were Catholic, you may have attended Fordham University, and again, your path would have been locked down from high school, as you would have attended one of the private schools in NYC that prepared students to pass Fordham's entrance exam.
However, if your father was a merchant or a businessman, you may have attended New York University's School of Commerce, Accounts, and Finance. Unlike Columbia and Fordham, NYU's founders were more interested in a young man's merit and ability, less so than his connections. But again, even at NYU, you'd be making connections from the get go and likely knew where you'd be working before the end of your final year.