が早いか => no sooner than; as soon as ~ N1
を契機に => as a good opportunity/chance to N2
Expected
を[機「き」]に => Use A as an opportunity N1
Time, Situation
が[早「はや」]いか => As soon as A occurred, right after A N1
Time, Situation
を[契機「けいき」] => As a good opportunity A, (do) B N2
Information, Report
をきっかけに/を契機に => with… as a start; as a result of; taking advantage of N2