On you other points, you clearly don't know what prediction means scientifically. A scientific theory has two parts, a mathematical/deductive theory and a physical interpretation of the terms of that theory. A prediction of the scientific theory is the physical interpretation of a deduction of the theory. If a prediction is confirmed by experience we say it is confirming evidence of the theory. (Note that this does not mean the theory is proved, a common fallacy.) If, however, experience shows a prediction to be false, the theory is false (or at least highly suspect, there may after all be something wrong with the dis-confirming experience).
Now that you understand that, you will see that our practical, or even possibly in-principle, inability to recreate the purported Big Bang does not mean the theory makes no testable predictions. As I said, it does make such predictions and these predictions have been tested and have confirmed the theory. One such prediction is the so-called cosmic microwave background. Another is the primordial distribution of the light elements.
One last minor point. You seem to have the mistaken impression that scientists have thought that the universe is shrinking. Again, this is ignorant. Everyone agrees, based on observations of distant objects, that the universe is expanding. What has been surprising is recent evidence that the universal expansion is now accelerating but was decelerating in the distant past.
Most scientists NOW agree the universe is expanding. They didn't always. And who knows if they'll continue to. Not so long ago, there was an overwhelming consensus among scientists that the Earth was cooling, and that we urgently needed to take action to keep it warm (I'm old enough to remember being taught in grade school that scientists had discovered that "the Earth is cooling and millions of people are going to die if we don't stop it"). Now the consensus is that it's warming, and debate centers on how much of that is human-caused, not on whether it's warming or not.
As you point out, passing one or more tests of predictive value doesn't "prove" a theory. The global cooling theory passed a lot of scientists' experiments supporting the correctness of the theory. But it was later found to be utterly wrong. That some scientists have run experiments testing the predictive value of little bits and pieces of their explanations for their Big Bang theory, puts that theory on the same footing as the global cooling theory in teh 60s and 70s. "Intelligent design" proponents also use experiments on little bits and pieces of things to support their theory. And clear falsification of their general theory hasn't happened yet, nor has there been clear falsification of the current version of evolutionary theory. The widely accepted theory that environmental effects on an animal can't be passed down to offspring in the form of modified genes, is teetering on the edge, as very convincing research on gene expression is showing powerful effects of in utero programming, directly correlated to environmental factors like diet and stress, which get passed down at least 2 generations (and quite possibly more) in the form of very different gene expression patterns.
And I have better things to do than outline chapters from basic biology texts for you.