어느새 => 어느(which, what) 사이(span of time)에 => before I knew it.
* 새 = 사이: a distance or span of time between two points in space or time.
* 어느새 is a contraction of 어느 사이에, literally "in some (unknown) time period (which has already passed)".
For "suddenly", we have a different group of words like 갑자기, 갑작스레, 급히, etc.