The universe initially expanded very quickly but not at the speed of light.
A university professor of mine[0] who was (perhaps still is) involved directly in international scientific efforts to examine the expansion of the universe once explained the speed of expansion of the universe to me in a way that made perfect sense.
Unfortunately I can't remember the precise details but the concept relates to a change in scale of the distance between bodies.
My best approximation is this: the measurable distance between two points can increase without either point moving if the nature of what is between the points changes.
You can pseudo-simulate the concept as follows:
1. Open Google maps at a reasonable "normal" scale
2. Affix two dots to your screen and take a guess as to the distance between them as if the dots were actually on the map
3. Zoom out the map quickly as far as it will go
4. Guess again the distance between the dots
The ground distance between the dots increases dramatically. One could argue that the dots moved apart at a great speed, possibly greater than the speed of light if the change in distance is sufficient.
Clearly we know that the dots did not move. The scale of what was between them moved.
During the initial stages of the universe things behaved very oddly.
