What is the best approach to get noticed at work without coming off as a know it all?

Complete your assigned work within the timeframe given and to the expectations of s syour superiors

For any work outside of your assigned area, mostly suggestions are always welcome so if you have the chance you can always suggest your point of view along with the reason why you think it may work.

Its not about how efficently or effectively you are working, for me team meetings is the place to get noticed. At the start of the meeting/discussion do not talk or give any suggestion. While the people are giving Ideas and suggestions make a plan out of it (end to end). Usually Bosses goes for a plan not suggestion. In this case you will be the only person with a plan.... cheers :)