There was very much a prediction of the Big Bang, before it was strongly supported by experimental evidence. This is what Penzias and Wilson got the Nobel prize

There was very much a prediction of the Big Bang, before it was strongly supported by experimental evidence. This is what Penzias and Wilson got the Nobel prize for. Their accidental detection of the Cosmic Microwave Background matched a prediction by Gamow, and others previously, and it was also used as evidence to rule out solid state theory. Does that mean it's the whole story? Of course not necessarily, and the Big Bounce isn't necessarily incompatible with these observations. However, I don't think the idea that the universe rapidly expanded at some point in the past is under any doubt. So this wasn't a model fitting the data. In fact it was an accidental observation which agreed with a model that had been suggested much earlier. The fact Penzias and Wilson weren't even looking for it makes it even more unbiased. Wilson, I believe, was also a solid state person (as were many prominent physicists in the 20s and 30s).