The USMC was a ground-combat force that was often available for "force projection" by the United States, and thus would be the closest force for use when an armed intervention was required quickly. During eras when the US Army was often small and "between wars", the USMC, while also smaller, was deployed around the world with naval units and to remote bases. It was often involved in battles, large and small, far from home.

An early, famous example would be the detachment led by Decatur on the "shores of Tripoli" to burn a captured warship.

A more extensive example would have been the use of USMC forces during the Boxer Rebellion. Marines were deployed early in the crisis to defend the international legation, along with other nations' forces; and additional US Marines, along with some Navy and Army personnel, formed part of the international relief force. Of course to an American character, the role of the US forces would have been prominent.

A USMC invasion of Guantanamo Cuba, during the Spanish American war, helped bring about the expulsion of Spain, independence of Cuba, and started an occupation of that harbor that continues to this very day.

The USMC burnished its reputation for regular combat, in more standard fighting during WWI, where the USMC fought as infantry along side other US units, as well as British and French allies. The most famous of these battles was Belleau Wood. This was more of a standard fight and not a raid, invasion, etc. However it did add to the reputation of the USMC as above-average soldiers. Supposedly the official German reports called the Marines at Belleau Wood Teufel Hunden, and "devil dog" remains a term of pride for Marines.

But most of all, a character in 1936 might have been thinking of more recent, small-scale, closer-to-home actions. Throughout the first few decades of the 20th century the USMC has deployed to several interventions in the Americas that collectively became known as The Banana Wars. Combining the fervor of the Monroe Doctrine's idea that the USA had a duty to impose order on the Americans and shield the new world from European interference, and blatantly pro-US-business goals, the USA's policy towards governments throughout the Americas varied from coercive pressure to violent intervention and regime change. The idea of "the USA sweeping in suddenly" was acted out by the USMC, in at least nine different nations over 30-some years, including a 20-year occupation of Nicaragua, bombardment and occupation of the city of Veracruz, occupation of Haiti for decades, support of the revolt that created a pliant Panama, etc. All of this would have been as recent to 1936, as the War on Terror would be today.

If this was Spielberg's work I would feel pretty sure that he knew about all this. But I don't know if Kasdan or Lucas would have been as meticulous about what a 1936 character would think about the USMC. All three were involved, so, forgive me if I want to see Spielberg's fingerprints on this. :)

From its roots in the Continental Marines who raided the British garrison at New Providence Bahamas and the Marines who marched a force of mercenaries 500 miles to liberate “The Shores of Tripoli” in the early 19th Century, the U.S. Marines had become widely known as “State Department” troops by the early 20th Century time period in which “Raiders” was set. This reputation was further burnished by numerous overseas engagements during that general time period that could be classified as “Small Wars” in which small deployed units of the U.S.M.C. protected American assets, personnel, and interests around the globe. The lessons learned during these engagements were consolidated in the “Small Wars Manual”, which is an official publication (FMFRP12-15) that was published just before WW2 and which remains a well known and valuable resource for counterinsurgency operations to this day.

A parallel yet more dramatic cinematic example of such realistic highlighting of the U.S. Marines in a storyline is “The Wind and The Lion”, written and directed by John Milius, and starring Sean Connery and Candice Bergen. This 1975 film came out five years before “Raiders” in the last quarter of the 20th Century. This film dramatizes events involving Teddy Roosevelt’s “Speak Softly, and Carry a Big Stick” foreign policy of the early 20th Century. There is a climactic scene in which a company of Marines boldly enters the palace of the Muslim “Raisuli” (Connery) and frees the captive American played by the lovely Mrs. Bergen. Definitely worth watching. Incidentally, Milius was also involved in later “Indiana Jones” series films (Temple of Doom), as was Sean Connery (Last Crusade).

From The NY Times Archives: “Based on a true incident, “The Wind and the Lion” is the story of Roosevelt's sending the Marines‐without invitation‐into Morocco in 1904 to rescue an American widow and her two children who had been kidnapped by the last of the Barbary pirates—a desert chieftain named Raisuli.May 23, 1975 Raisuli: Sean Connery Theodore Roosevelt: Brian Keith Eden Pedecarls: Candice Bergen John Hay: John Huston” https://www.nytimes.com/1975/05/23/archives/wind-and-the-lion-comes-to-music-hall.html

In 1917, there was a widely published U.S. Marine recruiting poster with the phrase, “Tell That To The Marines”, which was a positive turn on a formerly rather pejorative British phrase. FDR, whose son was a Marine Raider, used it in one of his famous fireside chats to counter Nazi propaganda. Ever since, the phrase has come to mean that wherever there is injustice directed at Americans, tell the Marines if you really want something done about it. Many movies, books, and television episodes have used the phrase in this positive context.

From its long history of excellence as an expeditionary military organization, it therefore seems clear that the characters depicted in both films would properly have been expected to know that the U. S. Marines could be counted on to conduct “Special Operations” type activities in the absence of a declared war and long before the existence of other specifically designated SpecOps units. “Send In The Marines”, and “The Marines have landed and have the situation well in hand”, have been a well-known phrases in the general U.S. lexicon for more than a century and for good reason.