The theory is that a period of inflation happened, during which the laws of nature did not apply. Inflation was much faster than the speed limit of light would allow. But even in present times many suspect that the universe is expanding and that the expanding is not governed by the speed limit of light. The idea is that space itself is expanding and carrying light along with it, stretching the light and causing the red shift we see.As I understand the question, the person is asking what was the ''initial expansion speed'' - inflationary phase occured after the big bang, but not too long after. Before the superluminal stage, space and time expanded at the speed of light. This does not violate relativity, as much as it does not violate it when it moves at superluminal speeds.
I would be embarrassed if someone thought I believed such silly nonsense; but it seems to be what most scientists believe.
Ludicrous speed
(https://www.thenakedscientists.com/forum/proxy.php?request=http%3A%2F%2F3.bp.blogspot.com%2F_PNVfoGbhv5U%2FSPR4bPJcUMI%2FAAAAAAAAAO0%2F6Nb2DpeoguQ%2Fs400%2FSpaceballs_Dark_Helmet.jpg&hash=8a5ba5f6963b1ae0928d25d37d3f94d8)
My brains are going into my feet!