The big bang theory is just that - a theory. It may even be mostly correct. The fact, though, that there are properties of the theory that don't meet observations doesn't necessarily mean that the physics are wrong. It may mean that the theory is incomplete.
As a lay person, I understand that. I also understand that the singularity referred to as the Big Bang is a mathematical concept from which our physical reality arose. But the mathematical concept was the result of attempts to explain observation data suggesting a single point of origin for the expanding universe.
There is no evidence that singularities can even exist in the physical world.
Yet, there is observable evidence that our physical world arose from a singularity... a singularity which occurred in a state we are unable to adequately describe.
Accepting the big bang as a singularity makes a whole lot of assumptions that are just that - assumptions.
True but what better explanations are there for known observations such as red shifts and background microwave radiation?