Not the first moment in time! (6)
I believe the answer is:
second
This clue is a double definition.
'not the first' is the first definition.
(not the first but the second)
'moment in time' is the second definition.
(I've seen this before)
(Other definitions for second that I've seen before include "Position of runner-up" , "Small fraction of a day" , "Back-up; short time" , "Support - a little time" , "A duellist's or boxer's assistant" .)