Initiate

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mid 16th century (in initiate (sense 2 of the verb)): from Latin initiat- ‘begun’, from the verb initiare, from initium ‘beginning’.

wiktionary

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Borrowed from Latin initiātus, perfect passive participle of initiō(“begin, originate”), from initium(“a beginning”), from ineō(“go in, enter upon, begin”), from in + eō(“go”).

etymonline

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initiate (n.)

"one who has been initiated" (in secret doctrines, etc.), 1732, from obsolete or archaic past-participle adjective initiate "initiated, instructed in secret knowledge" (c. 1600), from Latin initiatus (see initiate (v.)).

initiate (v.)

c. 1600, "introduce to some practice or system," also "begin, set going," from Late Latin initiatus, past participle of initiare "to begin, originate," in classical Latin only in the sense "to instruct in mysteries or sacred knowledge." This is from initium "a beginning; an entrance," also in plural initia "constituent parts; sacred mysteries," a noun use of the neuter past participle of inire "to go into, enter upon, begin," from in- "into, in" (from PIE root *en "in") + ire "to go" (from PIE root *ei- "to go").

In some senses the English word is a back-formation from initiation. Related: Initiated; initiates; initiating; initiator.