I would love to see something like the resurgence of the Age of Exploration in DC as it pertains to outer space; that'd be a really interesting "event direction" to take the line in for a year or two.
But funding a space colony of any kind would still be a ginormous endeavor. We're basically talking about creating a new city, country, or
world that's light-years away from any actual Terran jurisdiction. Who's going to shell out the money and labor for a project like that which will almost certainly have no revenue for decades if not centuries? The government? I dunno about the fictional DCU, but our real life space programs have been basically hemorrhaging money for the last decade or so.
They'd have to start small. Terraforming the moon might actually profitable in the longterm --
potentially an alternate fuel source -- especially considering that the League has already set up shop there.
Most aliens in DC and Marvel tend to think of Earth as a backwards mudball populated by overpowered meddlers (DC) and genetic timebombs (Marvel). Not that they don't wind up coming here in battalions anyway, but there's nothing really too appealing about this sector to your run-of-the-mill galactic empire.