True, the 262nd Infantry Regiment was an element of the 66th Infantry Division.
Acccording to my references, the remarks concerning the 66th ID are correct, in that the division was not present for D-Day operations. It would have still been in training back in the states at that time.
These U.S. Army Infantry Divisions and their related Infantry Regiments are credited with participation at Omaha Beach:
1st ID, with 16th IR, 18th IR and 26th IR.
29th ID, with 115th IR 116th IR * and 175th IR **.
* NOTE: The 116th IR was temporarily attached to 1st ID for the invasion.
** The 175th IR went ashore 8 June 1944.
Other elements included the following:
5th Rangers 741st Tank Battalion 111th Field Artillery Battalion 7th Field Artillery Battalion 81st Chemical Battalion.
All of the above went ashore on Omaha Beach on 6 June 1944, except for the 175th IR, as noted.
Sgt. Williams must have been in some other unit at the time of the invasion.
It is a real mystery, isn't it ?
As an afterthought, I guess that it would be possible that once wounded during the invasion, he could have been rolled over into a secondary unit following his recovery, possibly to the 66th ID.
Please feel free to get back to me if you need to.