a prefix used freely in English and meaning "not, lack of," or "sham," giving a negative sense to any word, 14c., from Anglo-French noun-, from Old French non-, from Latin non "not, by no means, not at all, not a," from Old Latin noenum "not one" (*ne oinom, from PIE root *ne- "not" + PIE root *oi-no- "one, unique"). In some cases perhaps from Middle English non "not" (adj.), from Old English nan (see not). "It differs from un- in that it denotes mere negation or absence of the thing or quality, while un- often denotes the opposite of the thing or quality" [Century Dictionary].
c. 1400, stertour "instigator; one who starts," agent noun from start (v.). Mechanical sense is from 1875. For starters "to begin with" is 1873, American English colloquial. Starter home is from 1976; starter set is from 1946, originally of china.
<a href="https://www.etymonline.com/word/non-starter">Etymology of non-starter by etymonline</a>
Harper, D. (n.d.). Etymology of non-starter. Online Etymology Dictionary. Retrieved $(datetime), from https://www.etymonline.com/word/non-starter