時刻 (shíkè) vs 瞬間 (shùnjiān) vs 時候 (shíhòu) for "moment"
Of these, only 瞬間 is really equivalent to moment in the sense of a brief period of time.


瞬間 means "a very short period of time, an instant".
時刻 can either mean "the time (of the day)", e.g. 5pm, or "constantly" (typically as 時時刻刻).
時候 can mean "time" in the sense of e.g. it's time to go. Alternatively, it can refer to an unspecified period of time, e.g. 小時候 -> when I was little.


There's a great deal of words that mean "moment" in the sense you're looking for. Here are some of the more common ones: 轉眼 霎時 剎時 剎那 瞬息 片刻 頃刻 一時之間

It is acceptable/common to append -之間 to these (e.g. 轉眼之間/霎時之間) to express the sense of something "happening within a very short period". Additionally, the character 一 (one) can be prefixed to some (一轉眼/一剎那/一瞬間).