Nascent is based on a root meaning “birth” and means “just beginning to come into existence.” It does not refer to “starting” in the sense of a game or a movie; nascent must refer to things that “grow” like a business, a project, or a life:
Tina worked hard to build her nascent career after graduate school.
Nescient means “ignorant, not-knowing”:
You will not find many nescient scientists!
Yes, nescient is related to the word science (which means “knowledge”).
Both nascent and nescient have a literary or intellectual style, and are usually avoided in casual conversation. And while nascent is a fine word to use, particularly in intellectual discourse, most English speakers are nescient of the word nescient; you’re better off using the word ignorant instead.