The biggest misconception I see in the question is the idea of the Big Bang as something that propagates "outwards", like an explosion. There is no outwards direction, the universe didn't expand into something.
Even though recent observations seem to suggest that the universe is closed, for the sake of simplicity let me assume that the universe is flat and infinite.
The first thing to notice is that if the universe is infinite now, it was infinite also at shortly after the Big Bang, it was just more dense. Imagine a flat plane on which it is drawn a lattice of dots, equally spaced.
The plane is the universe at a certain time. The dots represent objects in the universe, electrons, atoms, stars, whatever.
Now, imagine scaling up the plane, making it bigger. Of course the plane is infinite, so scaling it doesn't change its size, but the dots get further away from each other while keeping their size fixed (otherwise, you wouldn't be able to tell that an expansion took place).
You see that the dots aren't expanding into anything, the universe (the plane) was already infinite, it didn't grow in size.
Critically, there is not a center of the expansion. The distance from any two dots has doubled (in this example), regardless of their position.
Now, let's talk about the CMB. Imagine that at time $t_0$, every dot emitted a pulse, an expanding circular wave. This wave symbolizes the photons of the cmb that are emitted at the same time from every point towards every direction.
The last pictures refers to our situation. Earth is the black dot that is touched by the wave fronts. We see the CMB coming from every direction (in the picture only from four directions) because it was emitted from everywhere.