Unlike the stupid stories Jehovah's Witnesses sold as snake oil but claimed were divine, we Jews are not uncomfortable saying the following: "Some of our customs we attribute to God in the Bible are actually pagan."
That's kind of the reason why during the Babylonian exile the priests and scribes changed our historical narrative with a colorful liturgical folklore overlay of religious mythology when composing Bible stories. While this doesn't mean there might not have been some providence behind the events of Jewish history, seeing God's hand in things was more hindsight than anything.
What Witnesses see as a divine history in the Bible is actually a liturgical folklore, like American tales about George Washing chopping down a cheery tree in his youth, the midnight ride of Paul Revere, Johnny Appleseed planting American foliage, and Betsy Ross inventing the first American flag. None of this is fact, but these stories contain cherished truths among Americans. The Bible of the Jews was meant to be the same.
Circumcision may not have had heavenly origins. It may be more barbaric in its invention. Yet the Jews saw a providence in it once in Babylon on how it got woven into the Hebrew culture, and it along with many other practices was kept as a means to preserve our cultural identity. Instead of assimilation (as was the fate of most tiny cultures absorbed by Babylon), giving our cultural practices like circumcision a religious meaning through liturgy (that is the Scriptures) preserved us. Babylon, the mighty nation is no more yet we are still here.
Today some male converts to Judaism are not required to undergo circumcision in some circumstances. There are discussions among teachers about this practice. While I don't see it going away entirely, if at all, don't imagine for one minute that Jews are anything like Jehovah's Witnesses and blindly base their practices on the Bible.
If anything, it has always been the other way around.