From an earlier answer of mine

Informal agreements with the Soviets in the immediate aftermath of the war allowed for rail and autobahn access for each of the three Allies (US, UK, France) to transverse the Soviet zone to resupply their Berlin contingents. The Soviets and later the GDR honored these agreements in the aftermath of the failed Berlin blockade and this was how the various heavy equipment came into the city. The Western allies were able to get personnel and equipment in a series of scheduled convoys either by road or rail, with heavy equipment favoring the latter mode. he small size of West Berlin placed a natural ceiling on the amount of heavy equipment that could be deployed to the city. The only adequate area for tank training was Grunewald Park and the barracks structures were quite crowded.

This is not to say that military resupply or reinforcing the city was easy for the Berlin Brigades. Both the Soviets and the GDR sought to mire the convoys in red tape and other delays. The Military Duty Trains had to stop when crossing the inner German border and have their locomotives changed out for one by the GDR's Deutsche Reichsbahn, a needless waste of time. They were subject to various searches by the GDR's border police and this posed a problem for shipping new military equipment. When the British deployed their new Chieftain tanks to replace the old Centurions, the British removed top-secret equipment like gunsights, radios, and other sensitive materials before they were loaded on the West Berlin-bound trains. This equipment, along with the tanks' ammunition arrived via an autobahn convoy where the British could keep their eyes on it at all times.

The autobahn convoys were also the sight of various intimidation tactics and other unfriendly niceties to make resupply of the city less than easy. Stars and Stripes has digitized a 1961 account of one such convoy which conveys some of the minutia that typified a convoy. The convoys had to be completely self-sufficient, with the tools to repair any normal breakdown, and could not make any unauthorized detours. One British Berlin Brigade veteran recalled that the drivers for the convoys were all experienced men who were familiar with the route and would not make a wrong turn lest it start a diplomatic incident. The routine nuisances of bureaucracy became much more hostile during times of Cold War crisis, such as the during the erection of the Berlin Wall. David Hackworth's memoirs recalled when his unit was sent in as reinforcements during the erection of the Wall that the Soviet and GDR forces shadowed his convoy creating an apprehension that stopping for a cigarette break could start World War III. But the series of escalating and deescalating crises over Berlin had the advantage of allowing the Berlin Brigades to swap out older equipment for the newer material once their reinforcements left the city.

The long and the short of it is that sending in heavy equipment and reinforcements was not an impromptu affair. The equipment followed a pre-set route and Allied logistics made arrangements with their Soviet and GDR counterparts to ensure such convoys were not a surprise.