Lerner, Eric J., The Big Bang Never Happened,Vintage Books, 1991. I'm a bit dubious about his argument, since he appears to propose that the universe is infinite in both time and space. I think he dismisses Olbers Paradox too quickly (the night sky is dark; if the universe were infinite in time and space we would expect the night sky to be as bright as day).
Weintraub, David A., How Old is the Universe, Princeton U. Press, 2011.
Arp, Holton, Seeing Red, Apeiron, 1998. Arp argues that the "red shift" has nothing to do with velocity and the Doppler effect, but instead is a function of the age of the source.
Ratcliffe, Hilton, The Static Universe, Apeiron, 2011. The author argues that the universe is not expanding at all, but the red shift is due to light losing energy as it travels great distances, thus increasing in wavelength.
Obviously these books are at variance with the "standard model" of cosmology, but each points to discrepancies that the "standard model" doesn't explain.
I'm not a cosmologist. The arguments in each of these books sound plausible, and some seem to be supported by evidence. However, it's outside my field, and I can only say it sounds interesting and worth reading about.
**** “... he appears to propose that the universe is infinite in both time and space ...” ****
Like you, I’m not a cosmologist, but I believe that both are infinite. It just feels right.