Not sure I fully understand what you're trying to do, but it sounds to me like the elements you do and don't want to play should be on their own timelines. Convert each element into a symbol, and then you have more control over their playback, such as choosing an event that starts playback.
Just to complete Joe's suggestion, the symbols have an autoplay property that you should set to false.
To play them use:
To hide or show symbols: