Is there an easy way to find U.S Navy enlistment records?

I have learned that my great-uncle, now deceased, was stationed at Pearl Harbor in December 1941. Is there an easy way to search his enlistment dates and perhaps what his job may have been on that day? Some type of publicly availible search other than sending a request to the Navy?

You won’t have to send a request to the Navy, but you’ll have to send one to the National Archives.

Be aware that many, many records were burned and destroyed in the '73 Records Center fire.

Is this publicly available or do you have to prove ‘need to know or family relation’?