This question appears to have been answered by astronomers who have pushed the space telescope to its limits to identify the most distant galaxy ever observed. GN-z11 is 25 times smaller than the Milky Way, but it is generating new stars 20 times faster than our home galaxy. By measuring the redshift of the newly discovered galaxy, analysts have confidently dated it to 400 million years after the Big Bang, and only 200 million to 300 million years after the first stars began to form. To see even farther back, we will have to wait for the James Webb Space Telescope, currently scheduled to launch in 2018.

Orginally from:

http://www.spacetelescope.org/news/heic1604/

This illustration shows a timeline of the Universe, stretching from the present day (left) back to the Big Bang, 13.8 billion years ago (right). The newly discovered galaxy GN-z11 is the most distant galaxy discovered so far, at a redshift of 11.1, which corresponds to 400 million years after the Big Bang. The previous record holder’s position is also identified. Its remote position puts GN-z11 at the beginning of the reionisation era. In this period starlight from the first galaxies started to heat and lift the fog of cold hydrogen gas filling the Universe. The previous record-holding galaxy was seen in the middle of this epoch, about 150 million years later.