In 1915 large telescopes began to be built in the US which for the first time permitted looking at galaxies beyond our own. By 1929 Edwin Hubble's proposal that the Universe was expanding was established. This implied that the Universe must have been much smaller and much hotter in the remote past, since nothing else is known to intervene in gravitational expansion.
In the late 1940's, a Russian emigree to England, George Gamow and his student Herman Alpher applied some terrestial physics seriously to the expanding Universe. They studied the epoch when the Universe must have cooled for the first time to a temperature where neutral Hydrogen can be stable. Before this the Universe was fully ionized and photons could not move freely. But once the neutral Hydrogen formed the radiation would be free. Thus these were the oldest photons that could reach us today. If there was thermal equilibrium at this ``surface of last scattering'', then the radiation should just be lingering around, as a Planck spectrum. Alpher and Gamow's estimate of the temperature was 5 to 7 K. This proposal was not taken seriously for two decades since the means to make serious measurements of the microwave sky did not exist.