You cannot control, be in charge of, direct or even suggest expansion and colonization out into uninhabited space. Each and every time a new deep-space colony is founded, it has had to have been manually edited into existence by the devs. There's a whole empty galaxy out there, but you can't do anything about it other than explore it.
As an example, let's take a look at the community effort needed the last time a deep-space colony was founded: Obsidian Orbital, Maia.
As a community-driven effort, there was first
this thread in May 2015 to discuss the broad concept of colonizing the Pleiades and drum up support. Then someone else ran a "build a station inside a nebula" poll in August 2015,
here, with the Pleiades the clear winner. Then there was a CG to build and launch the new starport;
here's the Galnet announcement in Oct 2015, and the starport finally went live with version 1.5 of the game in November 2015.
So you see, at best, it takes six months to colonize a new star system - and that's with loud and long support from a broad base of players here on the forum. FD was at no time obliged to actually pay attention to the persistent requests to actually build Obsidian Orbital.