Actually BATF traces its roots way back there in history. Treasury established the IRS back in 1862.
In 1920 the Volstead Act was passed (prohibition) and the Prohibition Unit was established.
In 1930, the Bureau of Industrial Alcohol was created.
In 1933, the Alcohol Tax Unit was established.
In 1952, the Alcohol and Tobacco Tax Division was established.
In 1968, GCA68 was passed by Congress and the ATF was organized out of the ATTD.
In 2003, ATF was moved from Treasury to Justice and renamed BATFE.
The 4473 was an outgrowth of GCA68.