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].
late 14c., "reality," from Old French existence, from Medieval Latin existentia/exsistentia, from existentem/exsistentem (nominative existens/exsistens) "existent," present participle of Latin existere/exsistere "stand forth, come out, emerge; appear, be visible, come to light; arise, be produced; turn into," and, as a secondary meaning, "exist, be;" from ex "forth" (see ex-) + sistere "cause to stand," from PIE *si-st-, reduplicated form of root *sta- "to stand, make or be firm."
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Harper, D. (n.d.). Etymology of non-existence. Online Etymology Dictionary. Retrieved $(datetime), from https://www.etymonline.com/word/non-existence