TL;DR: The first prediction of the existence of "relict radiation" or radiation remaining from the "Big Bang" was made in 1948 by Ralph A. Alpher as mentioned in this paper, who developed the ideas of "hot" big bang cosmology to a high degree of physical precision.
Abstract: The first prediction of the existence of "relict radiation" or radiation remaining from the "Big Bang" was made in 1948. This derived from the seminal dissertation work of Ralph A. Alpher. He was a doctoral student of George A. Gamow and developed several critical advances in cosmology in late 1946, 1947, and 1948. Alpher developed the ideas of "hot" big bang cosmology to a high degree of physical precision, and was the first to present the idea that radiation, not matter, predominated the early universal adiabatic expansion first suggested by A. Friedmann in the early 1920s. Alpher and Herman predicted the residual relic black-body temperature in 1948 and 1949 at around 5 K. However, to this day, this prediction, and other seminal ideas in big bang cosmology, have often been attributed erroneously to the better-known George A. Gamow. This article reviews some of the more egregious and even farcical errors in the scholarly literature about Ralph A. Alpher and his place in the history of big bang cosmology. Two such errors are that (a) Alpher was a fictive person; or (b) that like the French mathematician Nicolas Bourbaki, Alpher was a "conglomerate" of theoreticians.
TL;DR: The early history of the CMBR is discussed in this paper, from its prediction in 1948 to its measurement in 1964, based on the published literature, the private papers of Ralph A. Alpher, and interviews with several of the major figures involved in the prediction and measurement.
Abstract: Much of the literature on the history of the prediction and discovery of the Cosmic Microwave Background Radiation (CMBR) is incorrect in some respects. I focus on the early history of the CMBR, from its prediction in 1948 to its measurement in 1964, basing my discussion on the published literature, the private papers of Ralph A. Alpher, and interviews with several of the major figures involved in the prediction and measurement of the CMBR. I show that the early prediction of the CMBR continues to be widely misunderstood.