Origins
To begin is to walk through a door. The word initial comes from Latin initiālis, from initium ('a beginning'), from inīre — literally 'to go in', from in- ('into') + īre ('to go'). A beginning was conceived as an entrance: the moment you crossed the threshold.
The Latin īre ('to go') is one of the most disguised roots in English. It produced exit (ex-īre: 'to go out'), transit (trans-īre: 'to go across'), circuit (circum-īre: 'to go around'), perish (per-īre: 'to go through completely' — destroyed), and ambition (amb-īre: 'to go around', from the Roman practice of canvassing for votes by walking among the citizens).
The noun initial — meaning the first letter of a name — appeared in the 1620s, from the medieval practice of enlarging and decorating the initial letter of a manuscript chapter. These 'initial letters' were often the most lavish elements of illuminated manuscripts, sometimes occupying a quarter of the page.
Figurative Development
Initiate preserves the threshold metaphor most clearly. To be initiated into a group is to be led through its entrance — ceremonially crossing from outside to inside. Ancient mystery religions made this literal: initiates physically walked through doorways, crossed symbolic boundaries, and emerged in a new state.
The PIE root *h₁ey- ('to go') connects initial to one of the oldest verbs reconstructable in the ancestor language, reflecting how fundamental the concept of movement is to human thought.