Both Uses

initiate
in
The Julian Chapter: A Wonder Story
(Edited)

It's the 'game' he initiated, where if someone touches Auggie he has to wash his hands....
p. 47.7

initiated = started
"And you know for a fact that it's Julian who initiated all this?" asked Dad.
p. 47.9 *

Definitions:

(1) (initiate as in: initiate discussions)
to cause (something) to begin
(2) (initiate as in: initiate into the art of drumming)
introduce to an activity or area of knowledge
(3) (initiate as in: initiate into the fraternity)
to accept someone's membership into an organization -- typically in a ceremony -- sometimes including a period of instruction and/or test
(4) (initiate as in: She is a new initiate.)
someone who has formally started in an organization, or been introduced to or attained some expertise in a particular field
(5) (meaning too rare to warrant focus)