Paradox to the Big Bang? If interested please answer

Is there a paradox to the big bang? What I mean is, there a lot of scientists and theorists who don't necessarily believe the big bang theory, but whenever I see science shows like for example through the Worm Hole that talk about "the size and shape of the Universe" "what is time" all of the theories shown are based off the assumption that the big bang occurred, aren't there suppose to be other drastically different answers based off the assumptions of other theories of how the universe began?

So in conclusion, are there scientists that don't believe in the big bang, but use it anyway to hypothesize?
Also if you do believe in another theory of how the universe was born tell me.

60 years ago, "Steady State" had a lot of following among cosmologists (notably Fred Hoyle). In the past 20 years or so, more and more evidence has accumulated that appears to best be explained by the "Big Bang" hypothesis. The current view is that there is dark matter that has increased the gravitational attraction in the vicinity of galaxies and galactic groups, and there is dark energy which is making the galactic groups accelerate away from each other.

Key pieces include things like the Cosmic Microwave Background Radiation, better measurements of the distances of far galaxies, and things like that.

Do remember that 100 years ago, our idea of the universe was that everything we saw out there was some part of the Milky Way. Hubble deduced that many of the then thought to be "nebulas" were in fact galaxies far removed from the Milky Way (about 80 years ago). With this much change in the accepted theories over the recent past, what can the future hold?

There are very, very few scientists who do not believe the big bang theory, because it is the only theory that explains why the universe is expanding today. The only one I know of who does not believe in it only mentions small and subtle details of the theory that don't make sense, and he has no explanation for the red shift of light showing the universe is expanding. He says that is up to others to figure out. So his arguments are weak in the face of that glaring omission. He seems like a smart guy but is definitely out of the mainstream of scientists. For one thing, he only has a bachelor's degree, not a PhD.