This sounds an awful lot like Behold the Stars by <PERSON>, which was published in 1965 per ISFDB. No serialization is listed, however.
This story was suggested as an answer (but not accepted) to this question, which does not seem like it as good of a match.
It definitely matches on the major plot points and concepts, particularly the "beachhead" of an invasion involving sending through materials to quickly construct new booths.
The part with the booth on a planet surface is a key part of the story:
He stepped out the far door, adjusting his body to the anticipated near free-fall conditions in the carrier and fell full length on his face, his body crushed down by a stunning and unexpected and altogether terrifying acceleration.
The breath had been thumped out of his lungs by the drop. He shoved up on hands and knees against the force dragging him down, feeling the blood pounding crazily behind his eyes, the drag on his muscles, the loosely sagging feel of his stomach muscles. Then all idea that acceleration was clawing at him was dispelled.
He was kneeling on a muddy ground, on earth and clay and a short squat mossy growth blotching that ground, and around his as he slowly rotated his head to look, dragging against that inexorable force, he saw squat scaled trees and dripping branches and dangling fronds of metallic creepers, and in his ears from his outside pickups the sound of dripping water and sloshing mud and the insane chirruping of some unseen animal life mocked him.
He was on planet!
... though it is quickly explained that the "box" was more likely placed on the surface by the enemy than that it had survived a crash:
How had the box come here?
The first and obvious answer lay in what <PERSON> had been saying: the carrier had been trapped by the gravitational pull of a small red star and had fallen onto the surface of a planet. But that was absurd. Even if the carrier had not been traveling at something like point four of c, even if it had just fallen onto the planet from a simple orbit, it would have been vaporized, smashed, utterly destroyed.
The boxes were built ruggedly; but even their armor couldn't stand up to that type of punishment.
So -- the box had been brought here.
The protagonist is involved in an ambush there but escapes back through, in a close call featuring the crushed hand that you remember:
The door began to close.
Two inches from the jamb the door hesitated. A hand -- a non-human hand with three fingers and a thumb clad in an armored mitten-type glove -- appeared around the edge of the door. The muzzle of a weapon snouted suddenly into view through the two inch crack.
<PERSON> flung himself sideways, jerked his exo-skeleton up to full power, stamped down on the retaining armored hand and heard the crunch as he mashed it flat.
The ending features the "General's" (<PERSON>) argument that peace with the aliens was only possible after an adequate show of force, which had now been accomplished:
"Major <PERSON> on the line, sir!"
"... cease fire. The Gershmi are sending in a truce party. Every indication is that they want to call a full-scale armistice. 322
Awaiting further instructions."
Marshal <PERSON> lumbered to his feet. His face beamed. "That's what I've been waiting to hear! Now we can talk friendship with the <PERSON>! Now we can talk about allocating the planets in dispute. We are two strong alien races talking as equals and neither side will suffer. We shall reach an equitable understanding." He walked around to the bowed form of Old Man <PERSON> and put a hand on his shoulder. "This is what you wanted, I know. So did we all. But there are right ways and wrong ways of getting it. Not until every single thinking being in space is prepared to be true friends with every other can your philanthropic wishes come true. Until then we must go on as we are, standing up for our own rights and respecting those of others."
"But war..."
"Is hateful and vile. One day we'll do without it. But with instantaneous matter transmission as the normal method of communication in the galaxy we're going to bump up against people still thinking in barbarous terms. We of Earth must be ready." 417