While he was at Carnegie Tech, aged 17, Buka read a scene for Alfred Lunt and Lynn Fontanne in an otherwise-empty theater. They invited him to join their company immediately, and he accepted. He toured with them for three years.[4]
Buka had worked on a film for Howard Hughes for three days when Hughes offered him a seven-year contract and told the screenwriter to expand Buka's part for the scenes that had not yet been filmed. Buka agreed to the contract with the stipulation that he be allowed to act on stage during the nine months of the traditional theatrical season each year.[4]
After some early experience in the theater, he got his start in mass media by appearing on the CBS radio program Let's Pretend.[5]