Why can we see the cosmic microwave background radiation? This radiation (CMBR) is said to have its origin at the surface of last scattering that exposed itself when the big bang universe had expanded for less than a million years.
In order to see radiation from a source, one has to be on its future light cone. In a universe that is flat and open, which our Universe is asserted to be at the large scale, we are not on the future light cone of this radiation, but almost maximally remote from it. One can also say that the surface of last scattering is not on our own past light cone. 
How is this visibility to be understood within standard big bang cosmology? 
(This question is different from an earlier one with the same wording.)
 A: One has to keep remembering that in the Big Bang model, the (0,0,0,0) is located in all points of the present day universe. Each of us is sitting at the center of the universe.
As the universe expanded all points expanded away from each other.

Light that decoupled from matter at 380.000  years after the Big bang, decoupled and left with velocity c from our points to wherever they were pointing when they decoupled. In our instruments we measure photons from the other parts of the universe that were pointing at us and which have undergone the doppler effect of the expansion. This is not radiation from a surface.
A: I get the feeling you think the CMBR is the flash from the explosion that was the Big Bang - like when Ripley blows up the Nostromo at the end of Alien.
If so, that's not really it. Rather, the universe was full of this radiation (heading in all directions) as it expanded. At our random position, we are now seeing photons that have been travelling for 13.7 billion years from a distant point in the universe. When they set out from that point, we were much closer (and they had a shorter wavelength), but as space expanded they had further to go to get to us.
A: The answer by anna v is in line with what I have seen previously, but is it clear enough? 
The "light cones" I mentioned can be shown in a graph in which one axis represents time and the other any spatial dimension. The scaling of the axes can be chosen so that a light cone is represented by a pair of lines inclined at +/- 45 degrees from the time axis. 
The future light cone of the radiation starts close to the zero-point of the time axis and is directed forwards. 
Our past light cone starts at the time axis much later and is directed backwards. 
I see no way of connecting two widely separated points close to the time axis by a 45 degree line without introducing closure or reflection. 
