It’s been fourteen years since the end of the second film. What really went on during that time?
If you take the original Evangelion canon as a recipe for the Third Impact, you need several elements. First is an Evangelion Unit with a soul and it must ingest an Angel to obtain its S2 organ / engine; this effectively gives the Eva unit unlimited power. Next, the Eva unit with a human pilot must merge with Adam to start the Third Impact. Once started, the human pilot must decide the fate of humanity's evolution. In End of Evangelion it is Gendou with Adam implanted into his hand who merges with Rei, however she rejects him and accepts Shinji as the leader for humanity's evolution.
In 2.x, the 10th Angel has already absorbed Unit 00 and is summarily defeated by Shinji. Unit 01 absorbs the Angel's core and Rei along with it. Although unexplained so far, it's assumed that Rei is in fact an “Adam's Vessel”, much like Gendou made her in EoE by placing his hand within her stomach. This would explain why Third Impact was initiated in 2.x which began the process of the destruction of the human race. However, Kaworu and Unit 06 stopped this process with a Lance of Longinus, in 3.x this event is called “Near Third Impact”. It’s assumed that, like the original series, Shinji is absorbed into Evangelion Unit 01 as a result of his abnormal synch ratio. He is resurrected fourteen years later and relabelled BM-03.
Here’s where it gets hazy as the aftermath of “Near Third Impact” in 3.x's chronology isn’t entirely clear. It is known that Tokyo-3 was decimated by the Third Impact, effectively exposing the GeoFront to the world, and that by raising Lillith's egg (located under the GeoFront) the world was ravaged by unimaginable catastrophes. A giant Rei, much like that seen in EoE, materialised within the control room of NERV and, like that movie’s Rei, it decayed where it stood.
It seems that in the aftermath of this failed Third Impact, either SEELE or NERV let loose a large number of mass produced autonomous units, likely powered by the Dummy Plug system, in order to quell... something. The remnants of these Evangelion units can be seen when Kaworu and Shinji explore the ruins of Tokyo-3. It's unknown what the white sphere that hangs above Tokyo-3 is; the canon would say that this is the moon or Adam's egg however the size seems to be inconsistent. Similarly the inverted pyramid that hangs high above the ruins of the world is what Shinji now refers to as the Geofront (thus why he and Kaworu had to descend rather than ascend to reach the ruins of Tokyo-3) though how and why it was raised is up for interpretation. It is possible that NERV hasn't moved and the world around it was destroyed, however it seems higher than Mt. Fuji which leads to the theory it was artificially raised.
At some point WILLE split from NERV (the latter taking on a cryptic and vaguely Sumerian logo), taking much of NERV's talent and the three Magi computers (or duplicates) with it. At a similar time Unit 01, likely deemed too dangerous to remain on Earth, was imprisoned with the torpid Shinji/Rei amalgam into a tesseract and launched it into orbit, much like Gendou saw fit to launch the Lance of Longinus in the original series. NERV remains as a shell with either an unseen crew or entirely automated with only Gendou, Fuyutsuki, Rei, Kaworu and then Shinji present within the decaying and voluminous base.