No, the tags were not affixed until June 15, 1976. It took years for the manufacturers after that date to get into the habit of posting the HUD label numbers on the data plate. So you will find late 1970 and early 1980 data plates without any HUD numbers--but everything else you need will be there, serial number, date of manufacture, address of manufacturing plant, snow and wind data, etc.
Prior to June 15, 1976 some mobile homes were constructed to a voluntary industry code but not all manufacturers and not all plants. Some manufacturers in some states would follow the code and in other states not follow the code. Also since the HUD code was first enacted in 1974--there will be homes constructed to the HUD code prior to June 15, 1976. But they still will not qualify for FHA, Fannie Mae or Freddie Mac because all of them only want homes constructed June 15, 1976 or later. Occasionally you will see the data plate--AKA Certificate of Completion on a pre June 15, 1976 mobile home. Those older Certificates of Completion will also have the plant address, date of manufacture and serial number.
Post photos of whatever documentation you found on or in the home.