By 1930, the redshift measurements of Hubble and others had convinced many scientists that the Universe was expanding. This suggested that in the distant past the Universe was smaller and hotter. In the 1940's an ingenious nuclear physicist George Gamow, began to take the idea of a very hot early universe seriously, and with Alpher and Herman, began using the hot big bang model to try to explain the relative abundances of all the elements. Newly available nuclear cross-sections made the calculations precise. Newly available computers made the calculations doable. In 1948 Alpher and Herman published an article predicting that the temperature of the bath of photons left from the early universe would be 5 K. They were told by colleagues that the detection of such a cold ubiquitous signal would be impossible.
In the early 1960's, Arno Penzias and Robert Wilson discovered excess antenna noise in a horn antenna at Crawford Hill, Holmdel, New Jersey. They didn't know what to make of it. Maybe the white dielectric material left by pigeons had something to do with it? During a plane ride, Penzias explained his excess noise problem to a fellow radio astronomer Bernie Burke. Later, Burke heard about a talk by a young Princeton post-doc named Peebles, describing how Robert Dicke's Princeton group was gearing up to measure radiation left over from an earlier hotter phase of the Universe. Peebles had even computed the temperature to be about 10 K (Peebles 1965). Burke told the Princeton group about Penzias and Wilson's noise and Dicke gave Penzias a call.
Dicke did not like the idea that all the matter in the Universe had been created in the big bang. He liked the oscillating universe. He knew however that the first stars had fewer heavy elements. Where were the heavy elements that had been produced by earlier oscillations? - these elements must have been destroyed by the heat of the last contraction. Thus there must be a remnant of that heat and Dicke had decided to look for it. Dicke had a theory but no observation to support it. Penzias had noise but no theory. After the phone call Penzias' noise had become Dicke's observational support.
Until 1965 there were two competing paradigms to describe the early universe: the big bang model and the steady state model. The discovery of the CMB removed the steady state model as a serious contender. The big bang model had predicted the CMB; the steady state model had not.