A special tool (called a locator tool) is required to assemble this, if you absolutely want to be certain the pin is at an acceptable depth, within the actual allowed tolerance. The tool usually costs quite a lot (it often comes in a set, along with other tools for cable assembly).
For this reason, if for whatever reason ready-made cables are not suitable, then often a better way to DIY cables (if that locator tool is not available) is to use a right-angle connector, because those usually have the pin pre-inserted, to the correct depth. The right-angle connectors can cost more though. Also, sometimes a straight connector is preferred of course.
Sometimes there are straight connectors with pre-inserted pins, designed like a turned-pin socket on the inside, for a friction-fit to the coax center conductor. I think I've seen those for larger RF connectors, I can't recall if that's a possibility with SMA or not. In any case, those sorts of connectors often cost a lot - more than a ready-made cable usually.
Also, it can be worth having an adapter (a good quality one) semi-permanently screwed onto test equipment, so that if there's a risk of a cable damaging things, then only the adapter is ruined, and not the test equipment.
EDIT: Incidentally, since you have a depth gauge, you could easily DIY yourself a locator tool. That's what I did, before I had a ready-made locator tool (although I guesstimated using other means, since I didn't have a gauge). To DIY a tool, you'd need to get a disposable SMA plug, insert the pin, measure it, and fix it in place (could bung the other end with epoxy glue. You may need to devise a way to keep it at the correct depth till the glue dries. Alternatively, replace the pin with say copper rod filed fully flush on the end, and solder it to the correct depth, using your gauge. Next, get a good quality SMA socket, torque on the shell of it to your SMA plug, and then insert a metal rod (again filed fully flush) into the SMA socket rear side, until it hits the pin, and then fix that in position (solder or epoxy glue). Now you can discard that plug. The socket becomes your locator tool.
Yet another approach is to get a machine shop to create a locator tool. But the DIY approach mentioned should work well I think.