en/dis-abling Dynamics in the projects settings is not the way to go at all (particularly if you want to do staggered objects later). Remove that and keyframe in the dynamics tag on the card (Cube in this case) and, in this case, either keyframe the Enabled parameter (unchecked/checked) or the Dynamic parameter (Off/On) when you want the cube to start swinging.
Dynamics will always require you going back to the beginning of the timeline unless you Cache the dynamics (Dynamics Tag/Cache) – there are options in there to cache all dynamic objects or only ‘this one’. Cached dynamics will play like you want and you will be able to scrub through.
Here’s an example with two cards, the left one is not cached and starts at frame 31 and the right one is cached and starts at frame 60. If you play it all should be ok but if you scrub through only the right one should work correctly.
11355_connectorwithdelay2.c4d.zip