I know people who are less than 5 years into their first jobs from graduation who are VPs in Engineering, in financial firms in London (City) and New York (Wall Street). Organisation/culture/industry matters more than subject, I think.

In my experience it's pretty rare to get the VP title in less than 5 years. In fact in my graduate intake nobody did it in that timescale. Good people would get it in 5-7 years.