When the Adam embryo first appeared, Kaji says "It's restored itself this far", and the case holding Adam says "he is living" on it.
Note there the container also says "Sample A-01", which could indicate there were "more" embryonic Adam samples (used for Project E?). Basically, what I am saying is that the embryo seen in NGE could have been one of several, grown from pieces of Adam after it exploded. In an old thread, someone also pointed out that this may indicate that the embryo was only one sample of Adam. Why? Kaji could have acquired "Sample A-01" from SEELE without SEELE getting nervous, because they also have at least one more Sample in their possession. As well, in Episode 24', SEELE says that "Adam's resurrected body is with Ikari", which is carefully worded enough to possibly exclude a reference to the "Original Adam" (which may have been destroyed during 2I). During EoE, Gendo says "We have both Adam and Lilith". He was not referring to the Evangelions, which theoretically are biologically equivalent to the Adam embryo. It's presumed that Gendo salvaged Tabris/Adam's soul after Kaworu died, and planted it into the Adam embryo. That's why he refers to it as "Adam" in EoE. We also see this elsewhere.
This also explains why in NGE, Lilith apparently lacks a Core. After Lilith underwent some sort of transition following the creation of Unit-01 and Rei, it may have lost its Core and appeared in its form in NGE. Following this train of thought, its quite possible that Lilith's "True Form" may have been similar to Adam's (I'll explain later).