By Jonathan Amos Science reporter, BBC News
IOK-1: Subaru has a track record for finding distant, early objects
The evidence comes from two new studies reported in the journal Nature.
One identifies a galaxy that is 12.8 billion light-years away, meaning it would have formed when the cosmos was about 6% of its current age.
It is the oldest observed galaxy based on an analysis of the way the expanding Universe has stretched its light.
Astronomers use a measure called redshift to describe this stretching - the expansion pulls the light out to longer, redder wavelengths - and IOK-1, as it is now known, has a redshift of 6.96.
Its detection has pushed current technology to its limits. The sky is generally bright at these infrared wavelengths and picking out individual, very faint sources is painstaking work.
IOK-1 was seen by Masanori Iye of the National Astronomical Observatory of Japan, and colleagues, who used the giant Subaru Telescope on Mauna Kea in Hawaii to survey a tiny patch of sky.
The second study, undertaken by Rychard Bouwens and Garth Illingworth of the University of California at Santa Cruz, employed the Hubble Space Telescope to gaze at an even smaller region of the heavens, just a millionth of its entire area.
They detected hundreds of galaxies out to about 900 million years after the Big Bang, but found just one unconfirmed "candidate" galaxy shining at 700 million years. (Current estimates have the Universe coming into existence about 13.66 billion years ago as a hot soup of elementary particles).
This paucity, however, does seem to fit with the generally accepted model that describes galaxies being built up in a series of mergers - from smaller to larger groupings of stars - in the first few hundred million years after the Big Bang.
"The significant result here is the lack of objects at high redshift," commented Dr Richard McMahon, from the Institute of Astronomy, Cambridge University, UK.
"Of course, what we really need to do is survey larger areas of sky, and that will give us brighter objects. The technology to do that will be with us within the next two years," he told the BBC News website.
Astronomy is now engaged in a major drive to tie down the timings of key events in the early Universe.
Scientists would like to see evidence for the very first populations of stars. These hot, blue giants would have grown out of the cold neutral gas that pervaded the young cosmos.
These behemoths would likely have burned brilliant but brief lives, producing the very first heavy elements.
They would also have "fried" the neutral gas around them to produce the diffuse intergalactic plasma we detect between nearby stars today.
From other observations, astronomers expect to see these first stars somewhere between a redshift of 8.6 and 13.6. This is between 570 and 300 million years after the Big Bang.
Dr McMahon himself hopes to get out to 7.7 and 8.7 with a new instrument called Dazle (Dark Age Redshift Lyman Explore). It will be fitted to the Very Large Telescope in Chile next month.
"Going after the very first stars will be problematic - it depends how bright they are - but certainly the first galaxies should be possible. These are galaxies with perhaps 100 million stars in them," explained Dr McMahon.
"The latest studies are telling us that there are galaxies at these very high redshifts and it is worth pursuing this work. It's difficult, challenging work but it's doable."
Even more advanced technologies are being lined up which will not only be able to detect these very faint sources but begin to probe their properties in some detail.
A refurbished Hubble telescope - assuming the US space agency gives the go-ahead for a final servicing mission - should be able to reach up to redshift 10.
Its successor, the James Webb Telescope, due for launch early in the next decade, is expected to get to redshift 15.