The earliest match that an Elephind newspaper database search finds for Martians in the sense of "inhabitants of Mars" is from a compilation of items headed "Inhabitants of the Sun," in the [Port Elliott, South Australia] Southern Argus (November 18, 1869), reprinted from an edition of Once a Week of some earlier date:
A French idealist, evidently suffering from telegraphy on the brain, proposes to the Academy of Sciences to establish communications with the peoples of the planets, if any such there be. His notion is to mount a great mirror upon the earth, and give flashing signals to Mars and Jupiter. He thinks that if these are repeated regularly, in batches of a certain number, the Martians or the Jovians, as the cases may be, will come to discern that they mean something, and will return them, and that thus a code will be eventually agreed upon, so that we may talk across the solar system just as we do across a field. This silly man calls attention to the bright spots which have occasionally been seen on some of the planets, and suggests that these were probably signals from the habitants thereof to us. This idea of planetary signalling is an o[d]d one; it has been mooted before, and (doubtle[s]s has occurred to thousands who have not had the effrontery to give their thoughts a tongue. My object in alluding to its present revival is to give an instance of the absurdities tolerated by the Paris Academy of Sciences.—Once a Week.
I haven't done a thorough search for instances of singular Martian in the sense of "inhabitant of Mars," but Martians certainly goes back to at least 1869.
Slightly older than the previous example is this instance from "Historic Progress and American Democracy," an address delivered by John Motley to the New-York Historical Society on December 16, 1868:
In popular periodicals and lectures of to-day you may learn much of the bays, rivers, inlets, oceans, and continents of the planet Mars; and if inclined for a vacation excursion, and could you find a conveyance thither, you might easily arrange a tour in that planet, starting from Huggin's Inlet and sailing thirty thousand miles along one of its very convenient estuaries without ever losing sight of land. I know not whether the Martians have accepted the nomenclature of Dawes Continent, Table-Leg Bay, and the other designations laid down on their planet by the spirited geographer of ours; but at least they might be flattered did they know of the interest they excite on this earth.