First, the regiment was at the front in combat within 90 days of the majority of their elements donning their uniforms for the first time. (O. W. Coursey - "Who's who in South Dakota: Volume 3" - Page 70)
They were used in the Advance during the Muese-Argonne Offensive. They had three platoons of the 2nd Battalion within the lead battalion advancing in the American column. (Robert Laplander - "Finding the Lost Battalion: Beyond the Rumors, Myths and Legend of America's Famous WW1 Epic")
In addition, once the Lost Battalion was found, the 53rd PI was used to inter their dead. (Thomas M Johnson & Fletcher Pratt - "The Lost Battalion")
The History of the 82nd Division tells that an entire battalion of the 53rd was detailed to bury the American dead from the Muese-Argonne Offensive. (James J Cooke - "The All Americans at War: The 82nd Division in the Great War, 1917-1918")
There is also a very good description of what the role of the few platoons of the 53rd were doing at the van of the attack (http://www.longwood.k12.ny.us/history/upton/302eng/craw8.htm).
Hopefully, I will have more details soon.