Space is unlocked at Civilisation level 3, it requires you to have completed Eden and built several Plane Wonders. You need to research the tech that allows you to "activate eden", once you've done that you will be able to enter the initial sector in space.
To be able to explore the first sector, you will need to set up your Airships for each of the four Factions worth of Gumballs at the same time. You can also add Robots and Clones to improve your total energy. Your energy will be significantly lower than in the Sky until you've done sufficient research. The 5th research tab which makes this possible is unlocked in the first space sector, M01.
The initial release for space brings one sector, more have been promised later in 2018 and following.