First great break-out

Humanity's first great break-out (PROSE: The Romance of Crime) occurred in the early 23rd century, following the 22nd century Dalek invasion of Earth which itself followed the initial Break-out of the late 21st century. (PROSE: Prelude Deceit)

In the post-Time War universe, following the Siege of Trenzalore, human historians were aware of stories which told that the Daleks reprised their invasion in the 22nd century but understood that, in any case, Earth eventually flourished in the aftermath, with humanity finally heading out to the stars to establish its own Empire, the First Great and Bountiful Human Empire. (PROSE: Dalek: The Astounding Untold History of the Greatest Enemies of the Universe)

In 2230, during the early years of the "first great break-out", humans colonised the Uva Beta Uva system located near the center of the galaxy. There, they settled on Uva Beta Uva Five, renaming it New Earth. (PROSE: The Romance of Crime)

A much larger Break-out, the Great Breakout, occurred in 5000. (TV: The Invisible Enemy) The Ninth Doctor told Rose Tyler that, by the 51st century, humanity would have spread out across "half the galaxy". (TV: The Doctor Dances) The dispersal of humanity allowed the evolving species to survive the natural destruction of their homeworld in the year 5,000,000,000, (TV: The End of the World) after which they made their home on a planet in galaxy M87 which they also named New Earth. (TV: New Earth)