The British were working on the .303 Browning around 1930?
They knew they could not use the Vickers gun in remote locations (where the pilot could not beat on it with gloved fist) and trying to use Lewis guns, even in multiple, was not going to be a long term solution either what with the 97 shot drum.
They had entered into negotiations for the Hispano gun in 1936 and were building the factory in 1938 so any scheme that advances the US .50 cal has to fall well before 1937-38.
View attachment 760309
This and it's classmates had been built to a 1930 specification with four guns desired.
It just took a while for adjustments to be made and factories built