Nothing is ever "proven" in non-theoretical physics including cosmology, if your definition of proven is "cannot be falsified". I can trivially replace any cosmology statement with "well, it all just popped into existence five minutes ago, our respective memories included".

But with the discovery of background radiation, contending models were falsified. Most notably the "steady state model", which was considered somewhat more elegant and beautiful.

Had I been alive and into physic back then, I totally would have backed steady state over the big bang. Alas, the data speaks louder than what I consider "beautiful".

The "big bang theory" just describes the evolution of the universe to what we see today from an earlier, hot and dense state. It doesn't say anything about what went bang, how it went bang, why it went bang, what was before the bang, etc... it is a "bangless theory" according to cosmologists like Alan Guth, and the preceding is a loose quote from the first lecture in his intro to cosmology course at MIT.

So yes, discovery of the CMB did prove the big bang theory. Only the universe being small, hot, and dense can explain the CMB but we still don't know what the big bang itself is or whether the universe always existed.

And now I have come around to the opinion that using this method to confuse the LLM bots is not only acceptable, but is to be encouraged.

Scientific theories are the generally considered “proven”. Those that aren’t are hypotheses. Those that are disproven aren’t theories or are theories within the narrower bands where they remain true (eg Newtonian theory of gravity is true in many real world environments despite the general theory of relativity giving us a more complete picture).

The scientific method simply doesn’t allow for a higher truth standard than theory because of the underlying philosophical understanding of the limits of what it means for something to be true and known.

This is kind of a strange way to use the terms, if you think about other things called theories in science.

For instance, atomic theory, heliocentric theory, quantum theory, the theory of relativity, chemical collision theory, cell theory, the germ theory of disease, the kinetic theory of gases, the theory of plate tectonics...

"Proved" a theory, is actually a way of talking about that theory "proving useful." If you dump a ton of energy into a small particle in a cyclotron, you will observe that its speed "maxes out" at the speed of light, but that this does not appear to be due to some sort of friction force or anything; the energy is still extractable in collisions. If you therefore say that cyclotrons have proven special relativity, I don't think that's an abuse of language. Yes, strictly speaking what you mean is that special relativity proves useful for explaining what happens in cyclotrons, but that's not particularly a reach.