You are after the 33rd Infantry Regiment, not 33rd ID.
Stanton's WORLD WAR II ORDER of BATTLE includes the following for the 33rd IR:
Stationed at Fort Clayton, PCZ, under the Panama Canal Department; moved to Trinidad, 11 Dec 41, under the Trinidad Base Command; arrived New York P/E, 13 Mar 44; assigned to XXI Corps; arrived Camp Cliborne, LA, 15 Mar 44, where inactivated 26 June 44.
Campaigns: American Theater without subscription, meaning that it was not combat engaged.
This was a separate regiment, meaning that it was never assigned to a higher element beyond XXI Corps.
I hope that this bit of imformation helps in getting you on track.
Please let me know if I may be of further service. OK?