In my experience (Brown undergrad), literally every undergrad I know who wanted to do research with a professor has gotten to. And usually they had plans on wor

In my experience (Brown undergrad), literally every undergrad I know who wanted to do research with a professor has gotten to. And usually they had plans on working with specific people by their freshman or sophomore year. And this is in fields as varied as Sociology, CS, Chemistry and Comparative Literature. Though, this may not be a function of going to a prestigious school, so much as a school that has 2000 grad students and 6000 undergrads, so professors are forced to interact and teach undergrads.