The transition is relatively easy. I did it the other way around back in the 1980's into the 1990's - Military to Automotive.
Note that a lot of the quality standards have been essentially phased out. The military uses ISO 9001 a lot these days (I think). But if the company is only specifying these they have some *old* contracts calling them out so I'd beware:
MIL-I-45208A - Inspection System Requirements
(Canceled)
MIL-STD-1520C - Corrective Action and Disposition System
(Canceled)
MIL-STD-45662 - Calibration System Requirements
(Canceled)
You never know. Those are the simple ones. I used to have several book cases filled with Mil Specs. I finally got my act together (since I don't use them any more) and threw them all out some years back.
The biggest transition will depend upon what field in the military industrial complex you want to enter. I have worked in a couple different explosives fields, high reliability (aka High-Rel) aerospace and marine electronics, communications electronics, and several other areas. The question will mostly be what your experience is in the specific area you will be working in.
Until you know what the product is and the processes are, you won't know what specifications and standards are applicable.
Also see:
I thought that MIL-Q-9858A, MIL-I-45208A and MIL-STD-45662 were obsolete
And BEWARE: Mil Standards in the US are free so don't pay for any. There are a lot of web sites that will pop up in a search which want to charge you.
My personal choice is:
ASSIST-Quick Search provides direct access to Defense and Federal specifications and standards available in the official DoD repository
Also see:
Looking for a copy of MIL-I-45208
Also, as a side note, you *may* have to get some level of security clearance. That can be a big can of worms. I wouldn't get back into the defense industry today for anything. I don't like FBI people hanging around and checking up on me. There's too much paranoia in the defense industry today for me to want to get involved.