Note that I am not an astronomer, and I haven't followed this very closely.
At one time, Alfven was given a lot of observation time at Palomar and other observatories, to allow him to find supporting evidence for his plasma theory. Most cosmologists were skeptical.
Alfven never did develop solid evidence, and I gather that the astronomers have grown a little tired of it. He probably has more difficulty now in getting telescope time. I think he is viewed as something of a crank.
The main criticism I have seen of the theory, is that the plasma should cause some degree of diffusion of the light, and this is not observed.
I don't think Alfven's theory is a promising alternative to the Big Bang. If you are a BB skeptic, I suggest you look elsewhere.