Alfred Cohen was born to Latvian-Jewish émigré parents in Chicago in 1920 and raised in the city. He showed a talent for drawing as a child and later attended evening classes at the Art Institute of Chicago. Shortly after he left high school the Second World War broke out and following the Japanese attack on Pearl Harbor in December 1941 and America's entry into the war, he volunteered for the air force. He served as a navigator from 1942-45 and was posted to Guadalcanal on the Solomon Islands in the Pacific from 1943-44 - an experience which profoundly informed his art.
After the war Cohen enrolled full-time at the Art Institute (thanks to the 'GI Bill', which paid tuition fees for ex-servicemen), where the teaching was dominated by the European tradition, especially French Impressionist and Post-Impressionist painting. Cohen set up his own portrait studio (together with two fellow students), painting celebrities including actors Basil Rathbone and Anthony Quinn - the latter became a close friend. Upon graduating, Cohen was awarded a travelling fellowship, which in 1949 took him to Europe to study in Paris for a year. He stayed on the continent for a decade, dividing his time between Heidelberg in Germany and Paris, and never returned to live in the USA.