I research at National Archives locations and specialize in Marine Corps. I've copied tens of thousands of pages of Marine docs on rifles and pistols and have been building databases of Marine weapons for a long time. There aren't a lot of Marine locations left that I haven't hit.
But I'm sorry to say there is about 0 chance that is real. All armorers and docs state they were not marked in any way with USMC as you describe. I remember maybe 20 years ago there was a guy that was famous for stamping USMC in stocks or metal and charging a premium. I'm fuzzy on that story, as it's been a long time ago. But I imagine it's a similar deal as this rifle.
If by some chance it was real. It would a one off and no way to authenticate it. But I really don't think it's real at all by your description.