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
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
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.”
“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.