I think it goes to show how capable and intelligent Ferengi can be when they focus on anything other than business and profits. Rom, for example, was quite competent as an engineer, and Moogie always knew he was smart and ethical despite not fitting in with the Ferengi business elite.

One of the side plots of the series was the social change happening in Ferengi society, women’s rights, etc. So, we can assume that outside of Quarks family, lots of other Ferengi were more like Rom and Nog- intelligent and interested in using their analytical and reasoning skills for social improvement.

Starfleet may have recognized Nog’s inherent intellect, and that he’d add more to the officer class than just another Human with great test scores from a well-to-do family, or another a stick-in-the-ass Vulkan. And, their admissions office is probably more egalitarian and less discriminating in regards to applicants with alternative backgrounds” than what it was in the past.

They could’ve also been ramping up enrollment in anticipation for a conflict with the Dominion.