It depends how far back into history you want to go. The important point is that the Maine Coon, or any other domestic cat in the North America, did not evolve from a small wild cat species in North America. Therefore all domestic cats in the USA are imported, non-native animals which irritates cat haters! It could have been different if a small wild cat species had evolved in North America which was suited to domestication. But there was and is no such cat species.
Therefore the Maine Coon was imported into America on ships from Europe, specifically probably England with traders and settlers. If there were aircraft in those days they would have been brought over on aircraft. That is how all domestic cats spread throughout the world from their point of origin which is the Eastern Mediterranean. FYI: domestic cats were imported into the UK with the Romans around 200 AD.
So Maine Coon cats are from Europe brought over to the state of Maine around 400 years ago. They were longhaired cats on ships or ship’s cats. Some cats “disembarked” and stayed on land where they found themselves living with farmers and others who liked them as companions and mousers. For hundreds of years these cats, before they were labelled “Maine Coon” cats, were standard random bred barn cats and home loving domestic cats like any other.
Back in those days there were no fancy pedigree domestic cats. They were indoor/outdoor cats doing their thing. Then the cat fancy started in England in the late 1800s. People had bred cats before then but formal, organised breeding began at this time. America followed soon afterwards. Handsome, shaggy farm cats called Maine cats became Maine Coons. The word “Coon” is an anomaly in my view. No one is sure where it comes from. There was a seafaring Captain Coon, it is said, who liked cats and let them come ashore in Maine but this may be fictional.
The first American cat show took place in 1895 at Madison Square Garden and a Maine cat, Leo, won best in show. If you wanted a shorter version of the answer as to where they Maine Coon cat is from it has to be modern day Europe. Europe was a bit ahead of America in those days with respect to domestic cats for the simple reason that it is nearer the hub where domestic cats were first created which as mentioned is the Eastern Mediterranean, the area now occupied by approximately Syria and surrounding areas (aka Fertile Crescent).
If you look at the original Maine Coons they are different to today’s versions. This is because of over 100 years of selective breeding by breeders who modified their appearance in a subjective desire to refine the cat. If you’d lived in the mid-1800s in America these domestic cats would have looked like any other. They were probably better days for the domestic cat except for the lack of veterinary care. This is because their lives were more natural. The most extreme selective breeding of Maine Coons takes place in Russia where they do extraordinary things with this cat. They look amazing and desirable but ultimately they are unnatural. It depends on what rocks your boat. I am a purist. I like to leave nature alone.
P.S. I wrote this out of my head. If you want to add or correct please do so in a comment. Comments are always welcome.