Hi Terri. The 336th was attached to the 5th Engineer Special Brigade in the UK on the 12th November 1943. The 5th was organised into three battalion beach groups, each group having a spread of specialists across the whole engineer spectrum. This was in preparation for D-Day.
They landed on Dog beaches between Les Moulins and Vierville (OMAHA) 6th June 1944. The 336th waded ashore at Dog Green and 1500 troops assembled at the shingle bank then proceeded on a hazardous march to Fox Red two miles away. The 336th ran into heavy machine gun fire and artillery shelling. This march across Omaha cost the lives of two men with 27 injured. The first job was mine clearance - your Dad was ashore in Northern Europe, under fire and very busy!
I hope this outline info adds to what you know.
Colin.