が早いか => no sooner than; as soon as ~ N1
[時「とき」] => At the time A N5
Time
と同時に => at the same time as; while; simultaneously ~ N2
Vた[時「とき」] => After having done something N5
Time
が[早「はや」]いか => As soon as A occurred, right after A N1
Time, Situation