時 also means "time."
「２時です。」 = "It is 2 o'clock."
「子供の時、テレビを見ました。」 = "When (I) was a kid, (I) watched TV."
「子供の時」 is like "the time of being a child" (I know it sounds weird in English).
If you want to say something like, "at the time..." I would probably use 当時 instead of 瞬間.
瞬間 means "instant" or "moment," so I think you could use it to say something like, "the instant I heard the phone ring, I knew who was calling." I don't know how to use this word very well, though.
当時, on the other hand, means "at that time" or "in those days."
「当時、よくテレビを見ました。」 = "At the time, I watched a lot of TV."
You're probably sick of the watching TV examples, but I tried to keep everything similar, haha! Hope this helps. But again, you may want to double-check with a native speaker. :)