Rome fell in 476 AD, according to the high school and World History 101 shorthand we are used to. You can prefer a date in the 370’s instead, or 410, or the Vandals taking Carthage in 439 AD, which broke the tax spine of the Western Empire for good. Going in the other direction, you can choose the collapse of the reconquest by Justinian in the late 6th C, or even later. If one wants to be really technical, Constantinople, the Eastern capital of the Roman Empire for a thousand years after Rome itself fell to Ostrogoths, did not fall until 1453. Few would pick that date, but you could, and make an argument with at least some facts to buttress it.
But let’s focus on 476 and let that hover in the background as we look at the collapse. In 440AD all looked bleak for the empire, though those in the central cities did not perceive it. Britain and Northern Gaul had fallen out of the empire. Northern Africa was a trading partner, not part of the empire. The influence over Persia, Syria, and the easternmost sections of empire was waning. Yet by 450, trading was bustling again. Some researchers would claim that this was actually the height of trade throughout the Mediterranean, unmatched for more than a thousand years. There was recovery! Despite all the dark portents, Rome reached its height. Arguably. Some would pick 150, 350, or other dates. Still, a case could be made.
If you were living at the time, those naysayers who pointed to the loss of tax revenue from across the Mediterranean, or the growing power of the Goths, who had an internal kingdom in Gaul, or the slow loss of border provinces and increase in cross-border raiding would be laughed off. However plausible their arguments might sound that the empire was in decline, the objective evidence was that things were fine.