Although it's still not clear what it means to ask for the etymology of the phrase, I can give some early examples of its usage. (Found through looking on Google Books for the 1600s. If you try this yourself, be sure to check the dates and not trust Google.)
Here's William Somner in 1640 (BTW, 'ſ' is the long s):
… their workes like themſelves ſpeaking Engliſh. The learned, I know, can further ſatisfie themſelves in the point from Bertherius in his Pithanon, and Morinus of late, in Eccleſiaſtica Exercitationes, not to mention divers others.
So here it's very much the literal meaning: there are "divers others", but they have not been mentioned. You can find many other usages of this type, where "not to mention" is not a rhetorical device of pretended omission, but used merely to point out that certain things have not been explicitly mentioned by name.
From here it's a small step (since the form is superficially very similar) to the many usages where the others are mentioned by name (a random example: this from 1698). (I'm not claiming this is how it happened, though.)
The rhetorical usage is also seen in a 1682 work by Robert Boyle, part of his disputes with Thomas Hobbes:
For, not to mention that it is ſtill by many learned men doubted whether the Terreſtrial Globe it ſelf have it; nor to examine whether or no he aſſigns a good Natural cauſe of it; it is not always true that… (p. 28)
For, not to mention that the Argumentation is invalid, unleſs by Fluidum he mean Omne fluidum, I reply … (p. 83)