Existence
late Middle English: from Old French, or from late Latin existentia, from Latin exsistere ‘come into being’, from ex- ‘out’ + sistere ‘take a stand’.
wiktionary
From Old French existence, from Late Latin existentia(“existence”).
Morphologically exist + -ence.
etymonline
existence (n.)
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."
