The first units at Ft. Sam Houston to be authorized issue of M1 rifles (FY 1936) were one battalion of the 9th Inf. (369 rifles) and one battalion of the 23rd Inf. (369 rifles).The first complete unit to be issued the new rifles was the 29th Inf. Regt. (1741 rifles), two battalions at Ft. Benning, one battalion at Ft. Sill. ( NOT the 29th INF. DIVISION. as reported in some publications. 29th Inf Div. was a National Guard unit prior to the war. Blue & Grey, MD and VA)
The regimental unit insignia on the hat looks more like the 9th Inf. Regt than the 23rd.
Source for this information (for all you non-believers out there); Third indorcement to AGO letter to the Chiel of Ordnance. December 21,1936, order of priority in issue of first 3370 semi-automatic rifles. note they were assigned priority prior to manufacture.