Theory and Analysis:S² Engine's Absence in Evangelions
Artificial Installation
It is possible that Adam and the Angels were equipped with Super Solenoid engines by the First Ancestral Race themselves, who created them artificially before installing them. This is especially likely if the Angels had been hidden all over the world by the First Ancestral Race, as opposed to being scattered by the cataclysm of Second Impact.
This would also mean that Nerv would have to create its own artificial Super Solenoid engines and fit them to Evangelions, rather than inducing their growth in the existing Evas. Since the Super Solenoid engine test used the engine recovered from Shamshel rather than one grown out of the Eva itself, this would appear to be the case at least for Nerv's Mass Production Evangelions.
Biological Generation
During Episode 20, a Seele member says that Evangelions cannot generate S2 engines by themselves, so biological generation is another possibility. Zeruel's devouring in Episode 19 reveals that the Super Solenoid engine is biological in nature, if nothing else.
Adam equipped the Angels
Adam might have carried Angel embryos within her own body, or they may have been present inside the White Moon. It is possible that during Second Impact, the Seed of Life Adam equipped the Angels with S2 engines, or the ability to generate their own Super Solenoid engines before she exploded.
Angels are innately capable of generating the S2 engine
Angels went through a prolonged gestation period in their eggs, during which time and in which environment they could have generated their Super Solenoid engines by themselves. Evas were built in a shorter timeframe and by an artificial process that did may not have allowed for the engines to be created naturally.
Eva Power Generation
Evas do have a limited capacity to actually generate energy(As opposed to converting it from one form to the other), as witnessed by Eva-01 and Eva-02 going berserk. It is possible that Evas can generate energy from their other organs using the same principles as the Super Solenoid engine, but that this power capacity can be used only under extreme duress, and they require a dedicated power organ in order to reach Seed of Life status.
