The first U.S. government customer was actually the United States Postal Inspection Service and the weapon was carried by agents to protect mail on trains and in trucks.
The United States Marine Corps had first tested the Thompson in 1920, but only in the mid-20s did the Corps finally commit to buying 700 of the new submachine guns. These were used during the Second Nicaragua intervention of 1927-1932, and in China. The USMC was the first to consider how an automatic, close-quarters weapon could be employed as part of a nine-man rifle squad, while the Army finally adopted the weapon in 1928.
As for the civilian market, the use of the weapon in the St. Valentine’s Day Massacre in 1929, as well as the fact that it was used in a few high profile bank robberies, including the 1933 Kansas City Massacre that left several FBI agents dead, suggested that maybe civilians shouldn’t so readily be able to buy the Tommy Gun.