This is going to be all about how kindergartens work.
The machines that were seen in the Kindergarten in On the Run are drill injectors. They drill deep into the earth and extract and cut gemstones into shapes and facets. They then inject the gem with Gem DNA and shoe it into a wall to let it incubate for a period of time. Once the incubation process is over and the new Gem takes its physical form, albeit much smaller and weaker than a regular Gem, they then emerge from their hole and begin training. They eventually reach a certain point of size and physical fazeek that matches a normal Gem. They are then released from the Kindergarten and put in the army.