Ah, so as the fella who wrote a novel and a novella tackling "Hitler without Goering" concept, I think I can take a stab at it. (Though in my works I did not kill Goering in WWI, and instead had him go off to Hollywood after WWI)
My take: without Goering, Hitler does not come to power in Germany.
Goering was vitally important to the continued economic viability of the Party by being the only early member of the inner circle who had connections to the rich and the powerful and who could ensure they would open their minds and wallets to the Nazi cause. He was the only one who could organize dinner-tables which eased Hitler into polite society by drawing on his extensive familial connections, war-time acquaintances (it pays to be the leader of the most famous flying squadron in the war, going back to HQ and meeting princes and their rich cronies at many occasions) and charisma. Goering and his wife provided the nucleus of these false-normal gatherings. No one else could have and no one else would have. Hitler at meal times came with three settings: mute, monologue and rant. Goering and his first wife could work around it and get Hitler to be seen and well received. It is very hard for me to picture Alfred Rosenberg pausing mid-stream in his "Vatican-Masonic defrauding the Protestant kingdoms" theories to inquire about the state of the veal of his princely dinner companion. Can anyone see Roehm doing well in these settings? Or Hess acting with any semblance of a human being? Jumping ahead, would have Himmler or Goebbels been able to arrange such things? Hitler's menagerie of awful creatures contained only one person capable of getting the rich and the powerful to appear at the dinner table - Goering.
Hitler gives Goering too much credit in organizing SA, largely to take the piss out of Roehm, but Goering did organize it and it was Goering who was entrusted with leading the foot soldiers of the revolution during the Beer Hall Putsch, no one else. Hitler understood Goering and knew he was seeing a walk-behinder. Goering could be counted out to organize and lead, on behalf of another, without eyeing the throne. Others were either too ambitious or too incompetent. Goering was the perfect mix of being competent enough, but so competent as to draw the ire of his master. Something Ludendorff did not grasp.
Goering was a cunning sociopath. Had he been born fifty years later, he would have been a Fortune 500 CEO or a serial killer, or both. He understood how to present himself to the public in ways only Hitler truly grasped. Even Goebbels for his brilliant and hateful oratory never got the masses. You can see it in the little doctor's speeches. As he whips the crowd into the ecstatic orgy of violence against the enemies of state, the runt takes a step back from the lectern, plants a fist on his hip and crooks an elbow, as if to mutter "sheeple." He was at once disgusted by the mob and entranced by his ability to feed its madness. Not Goering. Goering would spit hot fire and be carried with it, pounding the lectern and giving a show of exaggerated machismo which felt real and never once broke character. When Goebbels talked of waging Total War, people knew he wasn't going to be in the frontlines of it or fighting with them in the last ditch. When Himmler talked of being vigilant and punishing all miscreants it came with all the heat and sizzle of a man reading from a phone book. When Goering said every bullet fired from every gun would be his responsibility - the crowd roared. He gave them simplicity because he could fake simplicity and go along with it. Hitler's speeches were messianic, and distant. Goering's were immediate.
Time and time again, foreign diplomats upon being posted to Berlin would come back with a message of how Goering was the most normal of the bunch of the Nazi leadership. No one would have said it of Himmler, Goebbles, Roehm, Hitler or Hess. Or Ludendorff for that matter. Goering knew how to charm. Not many other Nazis bothered to learn it, and those which did not were not in the inner sanctum. Some were charming to fellow Nazis, which meant they could preach to the Inquisition, but Goering could speak to non-Nazis and be all things to all people. You can see it in his interviews at Nuremberg, which are a masterclass of disassembling and pitting one side against the other. To the British he said the Americans were nothing without their leadership and he knew the war was doomed because he knew he could not win the Battle of Britain. To the Americans he would say to not let the British steal your thunder, it was the Americans who won and he knew the war was finished as soon as they entered the war and he begged Hitler on his knees to not declare war on the Americans after Pearl Harbor. He even flattered the French. About the only ones he could not charm were the Stalinist Russians, because some things even the most cunning could not achieve. All this, with a noose soon to be over his neck. Contrast that with the interviews of the other broken creatures held in the same block. Goering understood how to manipulate people and his powers were much called up on before the Nazi grip on power was absolute.
Goering was crucial to organizing the SA, bringing connections to the Party, getting funding and staying loyal to Hitler in such a way as to get Hitler to regard him as loyal and keep him in place. Something no one else managed to achieve, before the Nazis came to power or had the electoral steamrolling momentum. Heydrich and Himmler showed up in position of power when the Party already held the whip hand. Goebbels was a schismatic and a late convert. Roehm was too enamored with the notion of the "socialist" aspect of the National Socialism and the idea of a revolution sweeping way "reactionary" elements. Rosenberg nearly wrecked the Party when left to his own devices when Hitler was in jail. And Hess was... Hess.
Hitler needed Goering.