In 1948, Ralph Alpher and Robert Herman (both in George Gamow’s team) came to the conclusion that if the universe had come out of a Big Bang and had expanded since that point in time, there should exist a cosmic background radiation in the frequency of microwaves (or what means the same, at a temperature of about 5K, 5 degrees above absolute zero). Alpher and Gamow had published that same year another prediction about the average composition of the cosmos, starting from the Big Bang theory.
In 1964, Arno Penzias and Robert Wilson were working with a newly built very powerful radio telescope and detected a background noise that could not be eliminated. First they thought that it would be of terrestrial origin, but once all the possible sources of noise had been taken into account, the effect persisted. Then they came to the conclusion that such noise could not come from the solar system or from our galaxy (for in that case it would be more intense in one direction than in another), and that its origin had to be cosmic. The temperature of that radiation (that is, its frequency, considering the Wien equation) turned out to be about 3K. Robert Burke of MIT suggested to Penzias that such noise could be the cosmic background radiation predicted by Alpher and Herman. This was in fact confirmed. For their discovery, Penzias and Wilson received the Nobel Prize in 1978.
Along with the argument based on the average composition of the universe, the cosmic background radiation gave the accolade to the Big Bang theory, which became the standard cosmological theory (although see an earlier article on this blog).