Enlistment is now and was back then 17 years old. Today you need parents permission to join since you aren't an adult. And you need to pass a GED or finish highschool early. Those rules were not into play back then.

US Code law, title 10. First enacted in 1956. Before that, USC began in 1926 and had very broad implications. Prior to that each service component did things differently with evaluating proof of age.

The opportunity to do so was there. Maybe someone else can expand and find more exact examples. But yeah, you need to go through all the USC to see that it was indeed legal to join as a 17 yr old and still is to this day. My first platoon sergeant joined when she was 17. God damn 37 years old and she had 20 years in to retire with a pension.