I did a bit more sleuthing... opened up the case again, and discovered that in what I thought was a bag of needles, were also two bobbins, a hemming foot, and the quilting attachments!
I managed to find the owner's manual on line, which is great because it explains how to care for the machine, how to thread it, wind bobbins and use the attachments.
The serial # is on the motor only and is 2B708408. I could not find anything on line indicating when it was made specifically. However, I did discover that National Sewing Machine made the actual sewing machine (and put the W.E. label on it) in their factory in Illinois, and Western Electric made the motor.
The motor is stamped with a patent date of May 22, 1917, and the website that told me about the mfr of the machine itself said that Western Electric stopped making these in 1918. So it seems that the machine was built in 1917 or 1918, and I may not necessarily find out exactly when.