Also, more specifically to how Starling initialization occurs, you can listen for the event
starling.events.Event.ROOT_CREATED which Starling will dispatch immediately upon creation of the object instance of your "Main Class" on the constructor.
After that, and from anywhere else in your app, you can get this instance by asking for
Starling.current.root (Note this may be null early on in app startup until Starling actually creates it.)
And as a final option, any of your Starling DisplayObjects that are living on the stage can also just query their
root property and this will also point to your your "Main Class" instance.