What did the big bang "look like"? I've been reading here for a while now and something I always see is people saying "the big bang happened everywhere" or "the center of the universe is where you are", explaning that the big bang didn't happen from a single point, but everywhere at once.
The problem is that I am unable to get an "image" of what that might look like in my head. What does it mean when the universe expands everywhere at once? I know that this might make sense from a mathematical point of view, but what would it actually look like?
 A: It probably is not possible for humans to get a physical picture of that time, because to do so would involve comparing it to something in the world around you today. But the Big Bang was almost certainly so completely different in it's "appearance", that we do not have words, past experiences or even intuition to help us describe it.
If it helps, we cannot describe an electron in any definitive physical way either, yet we are surrounded by, and composed of,  elementary particles.
In both cases, the best we can do is describe the Big Bang and electrons mathematically, which has worked out very well for us, and accept that trying to get a physical picture of either of the above is futile.
If someone claims that he/she has achieved an accurate mental picture of the Big Bang, or an electron, that they can relate to the "real" world, I  doubt that very many physicists would believe them.
A: 
I know that this might make sense from a mathematical point of view, but what would it actually look like?

Why not start with the data, which tells us what it actually looks like? 
The observations tell us that all galactic clusters are receding from each other. In an explosion in three dimensions, one could track the paths and find the center from which the explosion started. The observations tell us that they are all * receding from the earth*  There is no reason or evidence why the earth would be the center of a cosmic explosion! 
That is what gave rise to the "big bang" model,formulated in the four dimensions of time and space in General Relativity. 

Since Georges Lemaître first noted in 1927 that an expanding universe could be traced back in time to an originating single point, scientists have built on his idea of cosmic expansion. While the scientific community was once divided between supporters of two different expanding universe theories, the Big Bang and the Steady State theory, empirical evidence provides strong support for the former.

The center is at time=0, where the three space dimensions are also at (0,0,0) and a singularity that gave rise to the explosion observed . This singularity has been modified by introducing an effective quantum mechanical theory for gravity near this origin.
A: The argument that there is no center of the universe is only logically valid if the universe is actually infinite in size and mass or the universe is torus(aka it loops back onto itself(you would go back to your starting point if you traveled in one direction for long enough)). If the universe has finite mass and isn't torus then if you go in one direction for long enough you either see a gradual decrease in the density of matter or run into some sort of wall. In both these cases the shape of the universe would likely be a sphere. If it is a sphere, then the universe would have a center. That point would be where the big bang actually occurred.
