What event set the fall of Rome inexorably in motion, making it impossible to save?
The hoity-toity smarty-pants answer that gets you heads turning at fancy cocktail parties and eyes rolling in a college classroom is the Roman Empire’s fall became inevitable as soon as the Roman Empire became an empire.*
To more accurately address your post, this question is one that continues to spark hot debate. Gibbon claimed that it was when the empire adopted Christianity (pretty well debunked). Racists claim it was when the Romans letting in Germans (utterly ahistorical). Byzantologists get mad that you’re implying the Roman Empire didn’t continue in the east for another 1000 years (and then generally cite the fourth crusade or Manzikert as the major watershed event leading to the fall of Constantinople) and yet others cite the regionalization via construction of self sustaining walled cities and proto-manorial structures during the Crisis of the Third Century (honestly? Valid.)
In general, it’s just so hard to say. So many things just went utterly wrong for the Romans during the third century and then again after Constantine (many blame Constantine). I did a study a while back and found the average reign of an emperor before Commodus (many blame Commodus) was significantly longer than after Commodus (except the Constantinian dynasty).
When you talk about the rise and fall of a nation/empire, stability of leadership is incredibly crucial. The Romans, for all their bureaucracy and infrastructure and military accomplishments, never really figured that one out, even through 1453.
Cities would not have to become self sustaining if the Romans didn’t spend more time using their armies on each other than defending against raids and invasions. Goths and Vandals wouldn’t have been so eager to rip the empire apart if ambitious generals looking to score easy loot or political points were always poking them in the eye. The economy wouldn’t have been in shambles if the generals weren’t constantly bribing troops to support their long shot at the purple.
On a more macro level things really went past the point of no return probably when the Romans lost control of Gaul and then Spain. Losing Africa next was the last stop between survival and annihilation of the west. Though, all of this could have been weathered with smarter foreign policy and better, more stable leadership.
*there is a story that Scipio Africanus, upon sacking Carthage, wept because he knew that it meant Rome would one day be doomed