The idea of the Compositor is editing some kind of Input. Either the rendered result via Render Layer Node or an arbitrary image from your hard drive via Image Node.
At the moment it's only possible to set up an empty plate in the compositor via Mask Node.
Note: It's not necessary to use a Time Node (in your case), because it's also possible to animate the Fac value of the Mix Node, related: Is it possible Animate the Compositor node parameters?