Expanding universe and Big Bang Theory go hand-in-hand. There are multiple independent observations besides the red shift that make it nearly certain there had to be a BBT event to explain what we see. The universe is too hot, chaotic and clumpy for there not to have been a massive explosion to kick it all into motion. Since there is good confidence BBT happened, transitioning from that event to a steady-state non-expanding universe would require some sort of mechanism to slow then freeze the expansion. Not aware of any support for that model.