Not sure about the origins of Pershing's insstence on an "American" army; But our (industrial) infrastructure did an abysmal job of providing heavy equipment.

Most our artillery, and even some of our light machineguns (The Chauchat) were supplied by the French & British. Same for Aircraft, tanks, all the specialist equipment you need for combat. Patton had FT-17's (French Production), one Battalion of the AEF was equipped with British Heavy tanks.

The industrial mobilization for WW II ran on about the same time horizon, very limited quantities towards the end of 1942, suffency in 1943, (two full years in, not counting the long lead by foreign sales in 1939/40), and almost everything we needed in 1944.

Actually, the (two) African American Divisions were given to the French, clothed and equipped by them, and the Infantry Regiments used as fillers (Round out units?) by the French. (That's Eight Infantry regiments, Brigade equivalents today).