The collection on Ancestry is just the draft cards from the Fourth Registration (April 1942). The US had seven draft registration periods for WWII service.
This is from the Fold3 blog:
There were seven draft registration periods in the United States for World War II service. The first draft registration was held on October 16, 1940—before the United States had entered the war. Men ages 21–36 were required to register at their local draft board. The second draft registration was also held prior to the American entrance into the war, on July 1, 1941. This registration was for men who had turned 21 since the previous registration date nine months earlier.
The third (February 16, 1942) and fifth (June 30, 1942) registration periods expanded the ages required to register; the age ranges for the third were extended to 20–21 and 35–44, while the fifth extended them to ages 18–20. The sixth registration (December 10–31, 1942) was for men who had turned 18 since the fifth registration six months prior. There was also a seventh registration, known as the “Extra Registration,” from November 16 to December 31, 1943, which was for American men ages 18–44 who were living abroad.
I believe the draft records are in two parts: the draft cards themselves, and a series of classification ledgers containing summary details. The ledgers are held by the National Archives.
However, if I understand correctly, the later draft cards are considered 'personal information'. To obtain copies you will need to complete a Selective Service System Records Request Form (NA 13172), and provide either written authority for release, or a copy of your father's death certificate.
If your father served in the US Army, you may be able to find more of his enlistment records in the World War II Electronic Army Serial Number Merged File, available on the Access to Archival Databases (AAD) website.
This dataset contains some nine million War Department microfilmed punch cards on enlistments. However, it is far from complete. For more information, see the 2004 press release from the National Archives.
To search these records, click on "World War II" under the category section:
Then click on the Search button next to the Electronic Army Serial Number Merged File, ca 1938 - 1946 (Enlistment Records):
Fill in the form, using all the information you have, and click the Search button below the form: