If you want to become powerful in Galactic Age then you must understand economics.
Controlling space is nice but without having buildings it is worthless. The key is to build buildings to gather resources. Just make sure your repository is large enough to store all those resources you have piling in.
* Note: Resources don't automatically update you must refresh the page.
You can peacefully expand at anytime throughout the game all you need is enough resources and an open controlled section of space.