Therefore, it is at least incorrect to say that the microwave background confirms the big bang theory.
Well, the CMBR doesn't prove the BBT because no theory, for one reason, can be proven. A scientific theory must not only allow itself to fail, it must make predictions that would falsify it. But, if the predictions are discovered to match the theory, then the theory gets stronger. The greater the level of the prediction, the more impact it has on the theory.
The CMBR was predicted following the work of Gamow and Alpher who together determined that the universe must be mostly made of mostly hydrogen nuclei, assuming a hot Big Bang.
Not long thereafter, Alpher and Hermann realized that the BBT's expansion would allow the nuclei to allow electron, thus forming the first atom. They realized that such an event would stop the huge photon scattering and a CMBR would be observable. It was a huge prediction, but it took great effort to find it.
Inflation "theory" was added to explain only the smoothness of the CMBR, as well as the "flatness" problem.
According to the inflationary hypothesis, the hot universe was a plasma, and huge energy is needed to keep the plasma in a stable state, where did it come from?
The Hot BBT, unlike Lemaitre's cold version, gave us plasma. Inflation "theory" was not a temperature adjusting idea.
But, as you ask, where did all that energy/matter come from? It is likely beyond the purview of science since science is objective-based, where we must be able to test ideas with direct or indirect observations.