The USMC had protection detachments aboard all USN capital ships, and of course at the embassies, operating in the European theater.
The only major operation was from July 1941 to May 1942, the Occupation of Iceland after the British Operation Fork, by the 1st Marine Brigade (Provisional), consisting of 6th Marines (Reinforced) and 5th Defense Battalion.
Beyond that, there was:
Operation Torch (North Africa): the USMC provided about 30 men for training USN boat crews for the landing, and advising them during the actual landing.
Operation Overlord (Normandy): the USMC had two officers at Omaha Beach (observing NGS from the ships), one correspondent with the Royal Marines (aboard a LCG), one officer with Assault Force J, Canadian 3rd Division.
Operation Dragoon (South France): one interpreter for the French II Corps commander, one NGS observer aboard Nevada; plus landing parties of USMC detachments from cruisers Philadelphia and Augusta to formally accept German surrenders on three islands.
Operation Avalanche (Salerno): five USMC officers, each posted on a LST with British troops, one staff officer
Londonderry, UK detachment: from August '44 to November '45, 80 men were stationed in Londonderry to protect a Naval Radio Station, replacing the original "battalion" stationed there (which provided USMC support for the above operations).
London, UK detachment: varying between about 30 and about 60 men, joint ComNavEu and US Embassy protection.
There were also various "Marine Barracks" (company-sized FOBs) stationed around the Atlantic on British islands, e.g. in Bermuda or also Newfoundland.
And, afaik, there was a group from some Marine Nightfighter Group training with RAF pilots that later participated in Operation Avalanche.
The only USMC men to have actually come into a firefight in Europe would be the five men at Salerno and the one with Assault Force J in Normandy.