Of course we did, there was no other option.
Oh, but I forget that you do not know history so apparently are not aware of this little fact. After January of 1942, you could not "enlist" in the military in the US, even if you wanted to.
The entire process went to conscription, as it was the only way to control the massive influx they had. The military can only process so many people per week, and the easiest way to resolve that was to simply stop all "enlistments", and accept new recruits by conscription only. You could still go down and "enlist", all that did was select which branch of service and maybe what job you wanted. But once that was done, you simply went home and waited for your number to be called.
There was simply no other way to handle the over 16 million that were called up otherwise.
Only a very few could actually "enlist" during the war. Generally pilots, medical personnel, and those with needed foreign languages (specifically Japanese). They actually could enlist and go immediately to training. Everybody else, you just sat at home until you were called up.