Well, they didn’t really have much of choice. The only true alternative would have been to escalate the conflict into true, all-out war. Please note that during many episodes it came quite close to that.

Also, the Berlin Airlift was only necessitated by the Soviet’s cutting of the land connection. They believed that the Americans (and with them the British and French) would back down and accept a socialist annexation of The West Sectors of Berlin. They believed (not entirely wrongly assessing the mind-set in the West) that the US would be quite reluctant to enter war because of a seperated half-city filled with Germans which had been enemy’s until quite recently and which was impossible to sustain on its own.

But the Soviets underestimated the ingenuity and willpower of the American leadership (esp. Lucius D. Clay and the administration in Washington). They saw this as (a) the beginning of an avalanche of advancing communism and (b) as a clear break of the treaties of Jalta. Both views were quite accurate. There even was also plea by the freely elected mayor of west-Berlin which was clearly addressed at this direction in which he stated that should Berlin fall, the free societies in Western Europe and around the world would see and draw their conclusions. He famously said:

“Ihr Völker der Welt, schaut auf diese Stadt und erkennt, dass ihr diese Stadt nicht preisgeben dürft, nicht preisgeben könnt.”

(Peoples of the world - look upon this city! Realise that you mustn’t give up this city, that you CAN not give up this city).

Berlin was turned into a symbol, something JFK took up in his “Ich bin ein Berliner” - speech.

So why didn’t the soviets do more things to stop the airlift? First, it was thought that it wouldn’t work. They believed time was on their side, esp. when winter came around. They were not entirely wrong - it had never been done before and hardly was possible. Without technological advancement, smuggling and an unbelievable investment of resources and the perseverance of West Allies and Berliners alike it would not have worked. It was close call anyway (the trees of all the alleys which had survived the firestorm of bombing were felled for firewood in example). Also see the construction of the Tempelhof Airport.

Secondly the soviets were afraid to start a War because the US had the Atomic Bomb. The Soviet’s were close to getting their own bombs but they didn’t have them then.

So they tried to harass the planes, make life hard on them and used propaganda to try to dampen the spirits of the surrounded exclave. But that failed.

(Harrington, Berlin on the Brink. The Blockade, the Airlift and the Early Cold War. Lexington 2012; Udo Wetzlaugk: Berliner Blockade und Luftbrücke 1948/49. Landeszentrale für politische Bildung, Berlin 1998; http://verkehrswerkstatt.de/luftbruecke/; John Provan: Big Lift. Die Berliner Luftbrücke 26. Juni 1948 – 30. September 1949. Edition Temmen, Bremen 1998)

Greetings! This is an interesting question before us on the early origins of the Cold War in Europe, and it does seem a tad counterproductive that the Soviets simply allowed an entire airlift to occur without attempting to significantly obstruct or even entirely halt its progress. Let's see if we can establish the context of the airlift and its technical aspects, before then coming to a conclusion on why the Soviets did not simply stop the whole operation from becoming the major success that it did. Let's begin.

Note: I will assume for the purpose of this responses' brevity that you are already familiar with the basics of the Berlin Airlift.

Technicalities

When the Soviets enacted their blockade of Berlin in June of 1948, they shut down all road, rail, and canal entries into the city from the Allied zone of Western Germany. That they could do so was entirely legal, as none of the post-war agreements following the Potsdam Conference had sought the collective Allied control of such trade routes. In other words: no formal agreement guaranteed Western access by surface transportation. Because of this, the Soviets were acting entirely within their jurisdiction when they closed much of the passageways into and out of West Berlin. However, there was one form of transport that the Soviets could not shut down: air routes.

This was because in November of 1945, the Allied Control Council (the four-power body created to govern the Allied Occupation Zones of Germany and Austria after the war) approved the following action proposed by the Air Directorate:

"To confirm the proposals for the establishment of air corridors West of Berlin, as follows: BERLIN-HAMBURG, BERLIN-BUCKEBURG , BERLIN-FRANKFURT ON MAIN [sic]. Flight over these routes (corridors) will be conducted without previous notice being given, by aircraft of the nations governing Germany."

Approved at Berlin 30 November 1945.

Initially the proposal by the Air Directorate contained three additional cities beyond Germany, those being Prague, Warsaw, and Copenhagen. The Soviets later decided that only the three inter-German air routes would be required, and agreed to the maintaining of these three corridors with the rest of the Allied Control Council. Herein we find the critical guarantee for the air routes. The Soviets could not block the air corridors into and out of West Berlin from a legal perspective, because they had already agreed to allow the constant use of those three corridors to and from the Western sector three years prior to the Berlin Blockade. Now granted, there were still restrictions on these air corridors. The Allied aircraft had to fly between certain altitudes, and they were only twenty-six mile (41 km) wide corridors. If the Allied Aircraft strayed outside of these restrictions, then they were legally within the airspace of Soviet-controlled Eastern Germany, and liable to any sort of treatment the Soviet Air Force wished to apply.

It should be noted further that Soviet military aircraft did often fly alarmingly close to the transport aircraft throughout the airlift, and there were reports of Soviet aircraft actually opening fire close to airlift aircraft alongside anti-aircraft fire from Soviet ground installations across the route. The Berlin Air Corridors Incident Report logs 733 such incidents from the period of the 10th of August 1948 to the 10th of August 1949. However, as Major General William H. Tunner (Commander of the Berlin Airlift operation) noted:

"They [Soviet aircraft] were seen by the pilots and were sometimes close, but they were never more than a moral threat."

So then, from a technical point of view, the Soviets had to allow the Allied airlift to Berlin to continue without military opposition, because they had guaranteed safe passage along the air corridors which the Allies were using three years before the events of late 1948.

Other Attempts

Now the Soviets did attempt to prevent the success of the airlift through other means. Most notably, they made offers to West Berliners in late July and August 1948 that, if they came over to the Eastern sector of Berlin, they could receive free food and coal without any questions being asked. The idea was to 'entice' the West Berliners with signs of Soviet goodwill to an extent that they would not oppose (or even support) complete Soviet control of the Berlin sector as opposed to Four-Power control. This effort somewhat backfired on the Soviets: at the end of the first registration period (in which West Berliners could apply for ration cards in the Eastern sector), only 22,000 West Berliners signed up (less than 1% of the overall population of the West).

Further efforts did take place from October onwards, when West Berliners were offered to make a one-time pickup of coal and potatoes from so-called "Free Stores" in the Eastern sector. This campaign did see limited success, by March 1949 approximately 103,000 West Berliners were drawing food and coal from East Berlin (equivalent to about 5% of the population).

There were also attempts by the Soviet-backed SED (the East German Communist Party) in October and December of 1948 to wrest control of the city-wide parliament into their (and by extension Soviet) hands. These efforts failed however, and culminated in even greater shows of unity between West Berliners and the West. Most famously, a crowd of 500,000 spectators gathered near the Brandenburg Gate near the ruined Reichstag building in the British sector, with city councillor Ernst Reuter declaring:

"You peoples of the world, you people of America, of England, of France, of Italy, look on this city, and recognise that this city, this people, must not be abandoned—cannot be abandoned!"

Note: Pathe newsreels has an archive recording of this speech, alongside others given by West Berlin politicians on that day, on Youtube (accessible here).

So, to summarise:

"Why did the Soviets allow to American airlift into East Berlin to be so successful? Why would they allow it to occur at all?"

The Soviets could not stop the Allied airlift into West Berlin (not East Berlin) to be successful because they had previously agreed to keep the air corridors open without any exception. To do so would mean risking war, and neither the Soviets nor the Western Allies wanted to risk armed hostilities against each other after the destruction of the war they had just ended together. Though there were certainly military, economical, and political attempts to stop the blockade or to lessen its effect on the West Berliners' opposition to Soviet control of Berlin as a whole, these did not bear much success and were on the whole a fruitless effort. Hope this response helps, and feel free to ask any follow-up questions on this interesting event of the early Cold War as you see fit!

Sources

Brunhaver, John Steven. Lifeline from the Sky: The Doctrinal Implications of Supplying an Enclave from the Air. Report. Air University Press, 1996. 21-32. Accessed March 11, 2021. http://www.jstor.org/stable/resrep13825.9.

"Enactments and Approved Papers of the Control Council and Coordinating Committee." Volume I (1945). Accessible online (free) here.

Gaddis, John Lewis. The Cold War: A New History. New York: Penguin Books, 2005.

Kershaw, Ian. To Hell and Back: Europe 1914-1949. New York: Penguin Books, 2015.

Miller, Roger G. To Save A City: The Berlin Airlift 1948-1949. 1998. Accessed online here (free).

Stivers, William. "The Incomplete Blockade: Soviet Zone Supply of West Berlin, 1948–49." Diplomatic History 21, no. 4 (1997): 569-602. Accessed March 11, 2021. http://www.jstor.org/stable/24913337.