The Russian defeat at Tannenberg was anything other than inevitable. The Russian generals only needed to be slightly less miserably incompetent and stupid and the Russians would have suffered a far smaller defeat or even a victory. Tannenberg was singular in the whole of the war, there was no other encirclement of a large formation for the rest of the entire war, including of Russian forces that were far weaker than those at Tannenberg.
Tannenberg required the Russians to both attack recklessly, with open gaps between their armies and hanging flanks but also very, very slowly all the while carefully letting the Germans know where they were located and where they were going. The Germans also managed to assemble the 'A' team to oppose the Russian attack (Ludendorff, Hindenburg, Francois and Mackensen). Tannenberg would not have happened (in the sense that the entire army is surrounded) if:
1. The Russians had advanced faster - the timeframe for the German attack was marginal, too early and the Reserve corps was not in place and too late and the southern attack turns the German flank. A faster Russian attack leads to the narrow window closing.
2.The Russian flank defences had done their job - the flanking cavalry forces moved even more slowly and in the wrong direction, leaving the Russian commanders in the dark as to the threat to their flanks/rear. With a better flank screen the Russians would have had both more time to counter the attack, and/or withdraw. Either way capturing the entire army becomes less likely.
3. The Russians had actually communicated with each other - in any other army, or even with any other commanders the Russian forces would have been in a better position to support each other. It required commanders who wouldn't support each other combined with an overall commander who was grossly negligent in managing his subordinates and finally a supreme commander who lacked the ability to control/discipline his subordinates. There is no way, in any other army, in the entire war, that such a critical invasion would be left to the commanders on the ground to run with effectively no oversight from the next two levels of command.
If any of these issues had been fixed the Russian army would have likely survived Tannenberg, leaving the Germans outnumbered when they attempt to attack at the Masurian Lakes with a vulnerable flank still exposed. Anything other than a total victory in the Battle of Tannenberg leaves the German defences in a dangerous position, most likely forcing a retreat. Will this destroy the Germans in 1914 with the Russians in Berlin by Christmas? No. But it will change the balance of forces in the Eastern Front, leading to a different outcome.