The stone was just cabbed like that, a thin piece of turquoise. I have included two stones that have yet to be used in a piece of jewelry but already have the backing show.
I have included two bracelets from the time period you are mentioning. A couple of things that I notice is the difference in the way the silver looks, the image you shared looks like silver that hasn’t been worn and lost some polish. The cuffs I have shown have a true patina that is only captured with age. Also, look at the bezel. You usually find older pieces with a low bezel, maybe because the stones didn’t have backing. When I look through the old stones we have it is common to have no backing. Next, the craftsmanship. You didn’t have the number of silversmiths in the 30s - 50s that you do today. Most of them didn’t work at making jewelry full-time, and they also seemed to be concerned with craftsmanship. The pieces that I have included are much better made, a good example is to take a look at the bezel seems. I don’t know, it could be old. I just see lots of pieces and don’t think this is one of those old pieces, maybe something during the 1980s boom. It does have a good looking American turquoise that is not so easy to find anymore.