Shit shit this really feels like old mecha anime Where they used human brain to control the mecha
I think this one specifically is referencing specifically Evangelion.
Date-A-Live is has quite a few shoutouts/references to Evangelion
Ratotskr's logo is basically the NERV logo.
The whole city going underground and evacuate into shelter thing is basically from Evangelion.
AT Fields.. I mean Territories and only being able to defeat the Angels... I mean Spirits with said means (there are some differences since it's not a copypaste duh).
I guess some usage of the sephirotic crap (not as much of a link here) and thus some Biblical angel names.
A company with lots of influence around the world making special equipment that can use said AT... I mean Territories... with a hidden conspiracy to cause a supernatural disaster and wipe out humanity. Totally not like Seele amirite??
Origami is basically Rei Ayanami expy.
The concept of a bridge crew communicating with operatives isn't new so IDK about that one.
There's more similarities but obviously there are differences.
These are the ones I remember off the top of my head.