If you want the Rigid Body object to fall with gravity, you have to keep Dynamic enabled.
Go to the last frame where the Rigid Body object should be animated. Right-click on the Animated checkbox and choose Insert Keyframe (or click the dot on the right to set the keyframe).
Go to the next frame, disable Animated, right-click again to set a keyframe or click the dot symbol.
EDIT: As you wrote in the comments, you want to have a Rigid Body object not interacting with other Rigid Bodies until it is set to Dynamic. There is a setting which might help - it's not connected to the Dynamic setting so you have to keyframe it separately.
In the Rigid Body Settings further below you will find Collections (quite vague name, but the tooltip says "Collision Collections"). It looks like the Layers from older Blender versions. There you can select for each object to which "Collection" it belongs by clicking with LMB or Shift+LMB for multiple collections.
This whole configuration table can actually be keyframed, too. So, by default all Rigid Bodies are in the top left collection. If you now have one Rigid Body that should not interact with them until e.g. frame 50, then set it on the second slot. Go to frame 49, hit I while hovering your mouse over the table to add a keyframe. Then go to frame 50, select the first slot and hit I again. Now the object is in the same collection as the other Rigid Bodies and interacts with them.