I've read about Hubble seeing the brightest quasar in the early universe. Question is, how does science knows what is early and what is late?
Please correct me if I'm wondering, but after the big bang, everything went in all directions equally. How do we know what direction is the center of the big bang? And continuing on the line of thought, is "early universe" considered closer to the origin of the big bang or further away?
I assume you're referring to the recent press release about the quasar J043947.08+163415.7, observed recently using Hubble. The paper about the observations details how the authors measured the distance to the quasar, by calculating its redshift, a quantity that describes how the wavelength of light appears to change based on whether the object is moving relative to an observer. On cosmological scales, redshift can then be converted to distances. We usually see quasars at $z>0.1$.
As is usually the case, the quasar's redshift was determined by looking at spectral lines - in this case, Mg II emission around 21000 angstroms (see in particular the inset):
This emission line was observed to have a different wavelength than it would if the quasar was at rest, enabling the astronomers to calculate its redshift: $z=6.511\pm0.003$.
This is the typical process used to determine redshift, and therefore distance - well, not necessarily using that particular Mg II line, of course, but nonetheless the use of spectroscopy to measure how the location of spectral lines changes. The difference between "early" and "late" isn't quite clear, and probably varies depending on who you're talking to. For instance, someone studying the Big Bang might refer to the period before recombination as "early" - although we're seeing the quasar as it existed much later than that; it wasn't around for recombination.
I'd like to note that it's somewhat misleading to call this quasar the brightest (or even brightest known) quasar in the universe, because - as that press release notes - the gravitational lensing by a foreground galaxy, which enabled the object to be discovered, also magnified its brightness. It appears to have a brightness of 600 trillion solar luminosities, but without the lensing, that number is reduced to 11 trillion solar luminosities - a much more modest figure.
To answer the question "how does science knows what is early and what is late?" in simple terms:
We know that the Universe is expanding. Because of this, the light from things further away from us gets "stretched" more, and is redshifted. The bigger the redshift, the further the light has travelled. We can use formulas to work out the distance based on the amount of redshift.
The further away an object is, the longer it's taken for that light to reach us. So if we see an object with a very large redshift and we know this means it's very far away, the light must therefore have travelled a very long time to reach us. This is how we can tell whether the light comes from very long ago, i.e. earlier in the Universe's history. By examining the redshift of the quasar that you referred to, we can work out that the light we're now seeing was emitted 12.8 billion years ago, when the Universe was only 1 billion years old. That is amazingly early.
The "oldest" light we can detect is the cosmic microwave background (CMB) radiation, which you can think of as the "remnant heat" from the original Big Bang. When we look at its redshift we can calculate that the CMB photons started travelling towards us when the Universe was about 380,000 years old. We can't detect photons from earlier than that because the Universe was still full of free electrons, which scattered the light. As the Universe cooled enough for hydrogen ions to trap electrons and form neutral atoms, the "fog" cleared and photons were free to travel uninterrupted.
