Let's see what happens at the VA first. It may give indications of his previous unit(s). If so, then that solves that problem.
Once you get the pertinent information, then you contact NARA and request any information they have on the unit. They will perform a search and let you know what they have found. They will give you a cost estimate. Depending on what records they have, you may prefer to do it in batches.
You also have the option of going there yourself to retrieve records, have them copy so many, or even hire a research assistant to perform this chore. We can talk about that later...
A FREE option, yes FREE, is to contact the Army Corps of Engineer's Office of History. They will send you what they have. I obtained a lot of info this way. GREAT! 
Proud Daughter of Walter (Monday) Poniedzialek
540th Engineer Combat Regiment, 2833rd Bn, H&S Co, 4th Platoon
There's "No Bridge Too Far"