Do scientists first initiate neutron activity within the subcritical masses of fuel in the lab, or are the masses already undergoing some kind of minor neutron detachment naturally, or finally, is there no neutron detachment at all until supercritical mass is achieved?
The fission fuel in an atomic bomb is always undergoing spontaneous fission and hence emitting neutrons, but at a very slow rate. The rate stays slow in an untriggered bomb because the neutrons being produced are allowed to escape before they can trigger more fissions within the bomb material.
That bomb material is not pre-processed in any way to force it to emit more neutrons, but there are several neutron emitters which are incorporated into the design of the bomb to spray the bomb material with neutrons when the bomb is set off, to help reliably kickstart the fission process.
In nuclear bombs, initiators are typically used to produce initial neutrons, the initiators can be activated by a shock wave caused by conventional explosives.
Neutrons are introduced when the bomb is detonated.
The way it works is that (at least for a plutonium bomb), once the detonator is pressed, a very precisely machined and synchronized set of high explosives is set off around a plutonium core, which then compresses it to a density high enough to sustain the fission chain reaction (if the nuclei are too far apart, then the neutrons will not fission nuclei faster than they escape by [in a quantum sense] missing all the ones in the material). At the same time, a special neutron source, made just for this purpose, fires (this, again, needs ultra-precise timing as the shock wave from the chemical explosives is on its way and will soon destroy it) at the time the core is expected to achieve maximum density. These introduced neutrons then break up a few plutonium nuclei, releasing more and hence commencing the chain reaction.
It would make no sense to introduce neutrons earlier, because the fuel is either not dense enough to chain-react or, if it somehow were, then you'd kill yourself (and the town!) as that would blow it up right in the factory!