Your point is impressive, yet would be valid only if there was a beginning.
Not at all. Cosmic expansion and cosmic background radiation are not points to be validated or invalidated. They are observable, testable (and re-testable) pieces of data that science first predicted and then accurately described (and then further predicted, etc.).
The Big Bang is a conclusion, not a premise.
If stars have been living their life-cycles over a time period which has no beginning, in theory no time, than it would be expected that we could not see from whence the radiation came.
You misunderstand. Stars don't form, fly, or burn out willy-nilly throughout space.
They cluster.
More than that, and as I mentioned before, the speed of light is constant over all inertial reference frames. The further out you look, the further back in time you look. Given the model you are suggesting, we would expect to see the same radiation being emitted constantly throughout the universe. That isn't what we see. What we see is radiation coming from one point in time.
We also see every point in the universe expanding away from every other point in the universe.
The Big Bang theory describes these things very well. If you feel you must try to discredit a scientific theory that has challenged and re-challenged and come through it with all the more backing, you need to be able to find evidence that specifically contradicts it. If you want to replace the Big Bang theory with your own ideas, you need to
at least account for all the physical phenomena that the Big Bang accounts for and, preferably, phenomena that the Big Bang does not account for.
So far, you've done neither. Your claim that there is no evidence for the Big Bang is simply not true. (see wollery's description of your circular reasoning, re: evidence only valid if we assume a beginning point in time) Your alternative suggestion does not sync up with the evidence.