As far as I know, the first attempt to have a power armor for military use was made in 1965 by United States, being that the case, the science fiction concept predates reality.
Some science fiction stories showing power armor are Edge of Tomorrow (2014), Genesis Climber Mospeada (1983) and Tales of Suspense #39 featuring Iron Man (1963) . But which story was the first to feature one?
Which was the first sci-fi story to feature power armors for military use?
I would say the first instance of what looks like a power armor can be found in the second Hawk Carse story, The Affair of the Brains, by Anthony Gilmore (pseudonym of Harry Bates and D.W Hall), published in the March 1932 issue of Astounding Stories.
Here, Carse and his allies don three suits as they’re escaping from Dr. Ku Sui’s (the biggest threat to the solar system and Hawk Carse’s personal enemy) invisible asteroid.
At one point the authors explicitly say the suits Carse and friends found are powered:
“They might arrive famished, but in the power-equipped space-suits which Friday was lugging they should be able to span the gap”.
A few pages earlier, one of the characters involved had explained through which means these suits are powered:
“You’ll find the space-suits are equipped with small generators and gravity-plates (...) The switch and main control are in the left-hand glove."
In the next story, The Bluff of the Hawk (May 1932: the first four Hawk Carse’s stories are connected like parts of a single novel and tell a single story arc), we learn more details about these "self-propulsive space-suits".
First of all, they are spaceworthy:
“Thirty thousand miles was the gap between Dr. Ku Sui’s asteroid and Satellite III, the nearest haven (...) Thirty thousand miles in a cramped awkward space-suit grow into a nightmare journey, an eternity of suffering, and they will kill a good number of those who traverse them so”.
Later, a description is given, which includes a primitive gyroscope they are equipped with:
“His important weapon was the space-suit; therefore, he took it off and studied and inspected its several intricate mechanisms as well as he could in the carefully guarded light of his flash. It was motivated, he saw, by dual sets of gravity-plates, in separate space-tight compartments. One set was located in the extremely thick soles of the heavy boots; the other rested on the top of the helmet. He saw why this was. The gravity-plates for repulsion were those in the helmet; for attraction, those in the boot-soles. This kept the wearer of the suit always in an upright, head-up position”.
They're also so heavy that the wearer can only move thanks to their power source:
“The success of his raid depended entirely on keeping the two gravity mechanisms intact. If they were destroyed, or failed to function, he would be locked to the ground in a prison of metal and fabric: clamped down, literally, by a terrific dead weight! The suit was extremely heavy, particularly the boots, and Carse learned that the wearer was able to walk in it only because a portion of the helmet’s repulsive force was continually working to approximate a normal body gravity.
Although not full armors, these suits seem to be as resistant as armor:
“Swift fleeting batlike shapes would appear from nowhere for one sharp second, would beset him one after another in an almost constant stream, thinking his comparatively clumsy, bloated bulk easy prey, and then be gone. He snapped shut his face-plate under their assault. Sometimes there came different, more powerful wings, and he would duck in mechanical reaction, sensing the wings sweep past, often feeling them as, with sharp pecks and quick thudding blows, they sought to stun him. But the suit was stout; the repulsed attackers could only follow a little, glaring at him with fire-green malevolent eyes, then leave to seek smaller prey.”
And later:
“Without pause the lemak’s claws raked his suit. Unable to rend the tough fabric, it resorted to another method.”
Anyhow, these suits are not fully military (not yet at least) but para-military, so only one step before being possibly adopted by the military: they’re still a secret prototype, one the many technological wonders invented by the evil genius of Dr. Ku Sui.
Before Carse and friends stole three of them, these suits were used by Dr. Ku Sui’s lobotomized coolies only, his "guards": there are several pieces appearing over the stories, all of them identical (even the one worn by Dr. Ku Sui), so they’re not a single sample or two but look like kind of mass produced.
While Starship Troopers was definitely the first work that came to my mind, Heinlein may have gotten the idea of power armor from E. E. Smith's Lensman series. The first book, Triplanetary, was published in 1948. In the book, members of the Triplanetary patrol wear "space armor", e.g.
Through the aperture thus made Costigan could plainly see the pirate in the space-armor of the chief engineer--an armor which was proof against rifle fire and which could reflect and neutralize for some little time even the terrific beam Costigan was employing.
Although there are examples of "space armor" prior to Starship Troopers I am not familiar with any earlier instances of powered armor which reacts to and amplifies the wearer's actions.
To quote from the book:
The real genius in the design is that you don't have to control the suit; you just wear it, like your clothes, like skin. Any sort of ship you have to learn to pilot; it takes a long time [...] But a suit you just wear. Two thousand pounds of it, maybe, in full kit - yet the very first time you are fitted into one you can immediately walk, run, jump, lie down, pick up an egg without breaking it [...] and jump right over the house next door and come down to a feather landing. The secret lies in negative feedback and amplification. [...] The inside of the suit is a mass of pressure receptors, hundreds of them. You push with the heel of your hand; the suit feels it, amplifies it, pushes with you to take the pressure off the receptors that gave the order to push. [...] The suit has feedback which causes it to match any motion you make, exactly - but with great force. (Starship Troopers, chapter 7)
Without stretching the concept at all here is an example from 1955, four years before Robert A. Heinlein's "Starship Soldier":
"The Last Crusade", a short story by George H. Smith, first published in If, February 1955, available at the Internet Archive.
From time to time Coleman would lift the headpiece of his armor above the pile of rubble in front of us and take a quick look out over the big open square toward where the enemy was holed up on the other side. About half the time he'd draw small arm or automatic fire.
"Those birds must have infrared eyepieces too," he says as he sets down.
"Ah they ain't even got mecho-armor," I says.
"No, but they have body armor and helmets with quite a bit of stuff in them."
"I'll bet they ain't got anything like we got." I was feeling pretty fine right then thinking how much better off we was than the poor joes in the infantry. We don't just fight in our suits, we live in 'em. They ain't only a mechanized suit of armor, they're our barracks, messroom and latrine and all radiation and rain proof. We got more fire power than a company of infantry and more radio equipment than a tank.
"You know there's lots worse ways of fighting a war," I says. "You climb into one of these babies and they seal you up like a sardine but at least you're warm and dry and you don't even have to use your own feet to walk. You got a nice little atomic power pack to move you around."
"You couldn't move the legs of one of these things if you had to, the Sergeant says.
