Photo: Columbia Records (Copyright; All Rights Reserved)
Frank Sinatra records his first record:

July 13, 1939
On July 13, 1939, Sinatra recorded "From the Bottom of My Heart" with Tommy James and Orchestra.
Source: Daily Variety, 11/6/1992

Frank Sinatra's Application for the Major Bowes Amateur Hour, Library of Congress
Date Frank Sinatra made his radio debut:

September 8, 1935
On September 8, 1935, Frank Sinatra made his first radio broadcast with "The Hoboken Four," also known as "Frank Sinatra and the 3 Flashes," on the Major Bowes Amateur Hour talent competition, where the group won first prize.
Source: Library of Congress, 1/1/1900

  Date Frank Sinatra made his London debut :

July 11, 1950
Frank Sinatra made his debut at the Palladium. Of the performance, one critic said: "It was like being force-fed with treacle."
Source: , 1/1/1900