Space travel was a theme of proto-science fiction like Les Posthumes (1802) by Nicolas-Edme Rétif, Star ou Psi de Cassiopée: Histoire Merveilleuse de l’un des Mondes de l’Espace (1854) by C. I. Defontenay, and Lumen (1872) by Camille Flammarion, but these stories lacked any strong scientific understanding of what space was like or what space travel entailed. Some of the first actual fiction to deal with the actual science of potential space travel was Jules Verne's De la Terre à la Lune, trajet direct en 97 heures 20 minutes (1865) and its sequel Autour de la Lune (1869), which had the Baltimore Gun Club use a massive space gun to overcome gravity; H. G. Wells got in on the act with The War of the Worlds (1897), which involves projectile-ships, and The First Men in the Moon (1900-1901), where a gravity-negating mineral facilitates the travel.
In these early examples, the Earth-travelers are explicitly civilian, and the format of the story is that of the adventure-romance, a mode of fiction that would become known as scientific romance. Fiction of this genre would not always even bother with physical vessels for interplanetary travel; Edgar Rice Burroughs' A Princess of Mars (1912) involves a kind of transposition of bodies through space, much like Mark Twain's A Connecticut Yankee in King Arthur's Court (1889), and E. R. Eddison in The Worm Ouroboros (1922) used the same basic idea for his fantasy world (nominally Mercury).
Wells' War of the Worlds would involve an invading extraterrestrial force, but this not based explicitly on contemporary military structures, but a sort of inversion of invasion literature, where the technologically inferior Earth-forces are faced with a numerically inferior but technologically superior foe.
"Future war" fiction was another proto-science fiction mode, with close parallels to Yellow Peril literature and the like, and here we get closer to what might be the actual answer to your question. An unauthorized sequel to War of the Worlds, Edison's Conquest of Mars (1898) has the Earthlings repay the favor by invading Mars, with "Ships of Space" powered by a reverse-engineered Martian anti-gravity device and armed with disintegrator rays, and the immediate parallel is navel vessels:
From the northeast, their great guns flashing in the sunlight and their huge funnels belching black volumes that rested like thunder clouds upon the sea, came the mighty warships of England, with her meteor flag streaming red in the breeze, while the royal insignia, indicating the presence of the ruler of the British Empire, was conspicuously displayed upon the flagship of the squadron.
By the same token, The Struggle for Empire: A Story of the Year 2236 (1900) by Robert William Cole is basically the contemporary British Empire with its ships and fleets and colonies projected into space...and I mean that quite literally, it replicates the entire command structure of a naval fleet:
Early in the morning of the 12th of May, in the year 2237, the vast space of ground where the interstellar fleet lay drawn up was a scene of great bustle and excitement. The last preparations were being made, for in a few hours they were to dash off into space. The vessels were drawn up in long lines, being arranged in divisions, with the flag-ship of each division in the middle, and the other ships lying on either side of it according to their size and qualities. The flag-ship of the Admiral-in-Chief was floating about a hundred yards in the air, the Union Jack flying from one of its masts [...]
Not every story involving space-travel involved vessels, and not every vessel was military, but those that were military in this early period tended to be follow military lines of thinking - and there are real-life parallels to this, in the command structure of civilian merchant ships and (eventually) practical air travel.
The simile was sometimes carried over in other ways. "Space Marines" for example are first mentioned in "Captain Brink of the Space Marines" (1932) and "The Space Marines and the Slavers" (1936) by Bob Olsen; they rose to prominence with the space-transported mobile mechanized infantry in Starship Soldier (later Starship Troopers, 1959) by Robert Heinlein, which would in turn inspired the colonial marines of the film Aliens (1986).
In a lot of ways, it's fair to say that the idea of imagining space military forces based around terrestrial military organizations and forces is inherently flawed; writers and artists were drawing on what they knew - and as warfare changed and developed socially and technologically, this continued (and continues) to be true. The Star Destroyer from the opening of Star Wars (1977) is essentially an aircraft carrier in space, carrying multiple smaller attack craft (TIE Fighters) which attack or sortie in small squadrons, and which provide air cover for ground troops and mechanized infantry during assaults, as they did in The Empire Strikes Back (1980). The Vietnam War proved influential on David Drake's Hammer's Slammers (1979), reflecting his experience in the 11th Armored Cavalry Regiment.
Not all science fiction has explicitly followed this model; the military forces of Dune for example include both the presence of tactical nuclear weapons and effective deterrents; the initial stages of the military aspect of the conflict thus involve both references to traditional medieval siege and later 20th-century-style guerrilla warfare. The lack of specific military spacecraft (given the Spacing Guild monopoly) means that much of the rank-structure and organization is based on army ranks and command.
It’s almost entirely pop-culture derived and based on assumptions—space is “like an ocean” so the spacecraft would be like “naval vessels”. The reality is that space combat would look very little like naval combat. Space is cold and ships are hot—there is also no horizon to hide behind and seldom few islands (planets) to hide your ships either. Weapons will travel fast and damage will always be catastrophic. The goal of ships in space won’t be to dogfight like X-Wing fighters, but rather to get armies (let’s say the US Army’s first infantry division or “spaceborne” division, a natural evolution of Army airborne paratroopers) from one surface to the other as fast as possible. Time spent in space is time spent completely and utterly vulnerable to enemy gunfire which will absolutely cripple anything it comes in contact with.
Ideal spacecraft will be small and fast, not bloated capital ships filled with sailors. Space craft will also be tremendously devastating to life as we know it. Think about asteroids—imagine a ship the size of, say, a Star Wars capital ship flying full-speed into a planet’s atmosphere. You think kamikaze pilots and suicide bombers are bad? Imagine a space craft doing more damage to earth than the thing that killed the dinosaurs. And it wouldn’t even have to fire a weapon or even be manned—just slamming high-speed vessels into planets at high speed would be enough to destroy them.
Sci fi also (almost) always assumes Navy/Marines. There are exceptions, usually written by authors who really know their shit—but for the post part it’s always Marines = infantry, Navy = pilots. This is one of my biggest pet peeves, and not just because I have an Army bias, although that’s part of it... why is the US Army—America’s largest, oldest military branch responsible for ground warfare—always missing from the sci fi infantry battles in video games, TV and fine? Americans take for granted how large (unusually large) the US Marine Corps is. In reality, the Marines present a much smaller piece of the US military’s offensive capability than they are perhaps represented in popular media—particularly sci fi. The US Army has far more infantry, light, mechanized, Special Operations, or otherwise—than the entire Marine Corps. The biggest difference between the branches isn’t mission or function so much as it is strategic domain of operation. The Army is continental, and fights on the ground. The Marines are maritime, and deploy from the sea. Strategic domain is everything. So you can see why in sci fi, if space is an ocean, Marines and sailors are often your protagonists, even if in reality, that may not be the case.
Actually, as warfare advances, and as weaponry becomes more lethal, we’ll probably have less use for forces like the US Marine Corps and more use for US Army long range fires (think hyper-sophisticated artillery that can obliterate anyone on the planet fired from anywhere with pinpoint accuracy and scalable payload sizes). Infantry will still exist, as there will always be a need for humans to put boots on the ground and mop up, but the need for large armies—and large Navy’s Armies (aka Marine Corps) will dissipate. Think back to my example of a high-speed ship obliterating a planet by smashing into it. That’s the kind of long-range fires the Army could provide, from a planet or a planetary defense grid.
The reality is that the Air Force (as far as the US is concerned) leads space, and Army paratroopers are the closest force we’ve got to guys who deploy from aircraft to fight battles. That said, the idea of platoons of infantrymen landing and fighting aliens or other humans is unlikely to happen ever. As warfare advances, standoff weapons like long-range fires will become more nimble, accurate, and scalable. You won’t need space Marines for that.