In some senses the English word is a back-formation from initiation. Related: Initiated; initiates; initiating; initiator.
It forms all or part of: Abitur; adit; ambience; ambient; ambit; ambition; ambitious; andante; anion; cation; circuit; coitus; commence; commencement; concomitant; constable; count (n.1) title of nobility; county; dysprosium; errant; exit; initial; initiate; initiation; introit; ion; issue; itinerant; itinerary; janitor; January; Janus; Jena; Mahayana; obiter; obituary; perish; praetor; Praetorian; preterite; sedition; sudden; trance; transient; transit; transitive; viscount.
It is the hypothetical source of/evidence for its existence is provided by: Sanskrit e'ti "goes," imas "we go," ayanam "a going, way;" Avestan ae'iti "goes," Old Persian aitiy "goes;" Greek ienai "to go;" Latin ire "to go," iter "a way;" Old Irish ethaim "I go," Irish bothar "a road" (from *bou-itro- "cows' way"), Gaulish eimu "we go;" Lithuanian eiti "to go;" Old Church Slavonic iti "go;" Bulgarian ida "I go;" Russian idti "to go;" Gothic iddja "went."
c. 1300, "to start, initiate, cause to begin to be" (transitive), from Old French comencier "to begin, to start" (10c., Modern French commencer), from Vulgar Latin *cominitiare, originally "to initiate as priest, consecrate," from Latin com "with, together" (see com-) + initiare "to initiate," from initium "a beginning," literally "a going in," noun use of neuter past participle of inire "to go into, begin," from in- "into, in" (from PIE root *en "in") + ire "to go" (from PIE root *ei- "to go").
From late 14c. in intransitive sense "come into existence, begin to be," also "enter into a new state." Spelling with double -m- began in French and was established in English by 1500. Related: Commenced; commencing.
1580s, from French initiation or directly from Latin initiationem (nominative initiatio) "participation in secret rites," noun of action from past-participle stem of initiare "originate, initiate," from initium "a beginning" (see initial (adj.)).