> Could Germany really have beaten Great Britain, the United States and the Soviet Union all in a war at the same time?

The TL;DR of this is "No".

To answer the question more clearly, we need to have a look at what the military goals Germany was. Very broadly, the primary goal in 1941 was to force the Soviet union to surrender. That being done the plan was to either divert further resources towards the UK and either force them to surrender by means of an invasion or, more likely, accept a peace deal with Germany. At this point the idea was that the US would feel that a war against Axis powers that occupied virtually all of Europe and Asia was unwinnable and would also accept a peace deal. No peace deal with the Soviet Union was ever, to my knowledge, considered. So how likely was that?

In hindsight, the answer is not at all. The German military objective of Unternehmen Barbarossa was the so called A-A-line. An imaginary line going from Arkhangelsk in the north along the Volga to Astrakhan in the south. That would place basically all of the heavily populated and developed parts of the Soviet Union under German control and with Germany in control of oil fields, industry and major centers of population in the west and Japan pushing in from the east the Soviet Union would basically be caught between a rock and a hard place and forced to surrender. The plan itself was broadly outlined in Führer Directive 21 which is in turn based partly on the Lossberg Study by Erich Marcks. Now, Marcks was a WW1 veteran and the plan was in part based on the experiences from WW1. It vastly underestimated Soviet capacity to replace men and equipment lost which had been the case in WW1.

The lynchpin of the entire thing is that while Russia stood and forced Germany to commit upwards of 80% of its military resource to the eastern front, the allies were unlikely to listen to diplomacy. So how close was the Soviet Union to surrendering? Probably not very close at all. While the Germans initially made enormous gains in the early days the fortunes of war rather quickly turned against them. The German advance lost momentum as supplylines stretched beyond their breaking point. Operations were simply not feasible due to a lack of fuel, resupply and reinforcements. Every day the German army did not make significant gains the Soviets reorganized and reinforced. More and more Divisions fielded and moved into position. More and more war materials were produced and supplied via the lend-lease. Basically, every day the Soviets were growing stronger and the Germans were at best maintaining the same strength.

If you want a specific date, I would argue that the war was definitively lost for Germany not on December 7th (Pearl Harbour) or December 11th (US and Germany both declare war) but on October 31st of 1941. But, this is something I argue with the benefit of hindsight. When Operation Typhoon was halted it was over. Had Moscow fallen then perhaps, just perhaps, the situation would have developed differently. Supplying St. Petersburg would have been much harder. The Russian army would have to retreat further east to the area around Gorki and maybe, just maybe the war would have developed differently but in all likelyhood, it would not have. Taking Moscow wouldn't change the fact that Germany was unable to adequately supply its army. Yes, it might have taken a little longer but the 30 division of trained Siberian infantry would still have arrived, equipped and trained in winter warfare, the only difference is that they would have been forced to group further east before counter-attacking which might have delayed things. 1000 new tanks would still have arrived in the next month. 1000+ new planes would still have arrived.

Germany still resumed offensive operations on November 15th and while their armies had reorganized they had not been sufficiently resupplied or reinforced. The advance was no longer the sweeping attacks of the summer but a grueling crawl forward met with ever increasing resistance and ever worse weather. The supply situation affected the Soviet armies too with winter clothing in particular being a problem but not nearly as bad as it affected the Germans. The Siberian division in particular were well equipped and used to operations under these condition. Nevertheless, the German army advanced, slowly. Crossing the Moscow canal and looking like it might, for a while, actually encircle Moscow from the north and south. However, the closest the two German pincers ever came to linking up is ~80 kilometers. Now, that may not sound like much but at this stage German spearheads where only advancing 5 km a day, 10 at best, against stiffening resistance and with increasing threat to their flanks. In many divisions 80% of the vehicles were inoperable or lost and many regiments were down to below 200 men, effectively companies. In essence, many German regiments were effectively company strength formations and many divisions little more than regimental strength formations.

On December 5th the Soviets counter-attacked. Over a period of 32 days they drove the Germans 100-250 kilometers back, nearly encircled the Third Panzer Army and successfully encircling the XXXV Corps. At this point, in hindsight, there was no longer any hope for German victory. By spring of 1942 the German army had gone from 162 divisions capable of offensive maneuvers (the rest being garrison division etc) to 58. While the Germans managed to muster the strength for Case Blue in the summer of 1942 it was not successful and further depleted German reserves and supplies.

By the summar of 1943 the Soviet industry alone was out-producing the German counterpart in most areas. It is doubtful if Germany could have stopped the Soviet advance at this point even had the allies never landed in France. The Germans tried again to regain the initiative in 1943 with Unternehmen Zitadelle which ended with the disastrous Battle of Kursk. By now it was not even a question of organized defense or even a fighting retreat for the Germans, it was a constant mad dash to the next river that would slow the soviets for a while.

By 1944 Operation Bagration virtually destroyed what was left of Army Group center and from there on the Soviets had their sights firmly set on Berlin.

Sources:

The Soviet Economy and the Red Army, 1930–1945 - Walter S. Dunn
The Second World War on the Eastern Front - Lee Baker
Absolute War: Soviet Russia in the Second World War - Chris Bellamy
Moscow 1941: Hitler's first defeat - Robert Forczyk