I know that the Roman empire didn't dissolved overnight, but were there a certain period in which a Roman citizen could just say: well, everything changed around here, from now one, nothing will be the same again? And if the answer is yes, was this change something that a citizen would worry about? Or the transition was to slow for a generation to regard it as a collapse?
On a broader level, can the collapse of a civilization be experienced by individuals, or it's a lengthy process that overcome one's lifespan?
It obviously differs from region to region, as they were lost at different times.
I'd interpret the question as "when did almost every Roman citizen realize that the times, they are a' changing?"
While this is speculation on my part, I feel like the loss of the rich Eastern provinces and Egypt to the Arabs, and the subsequent failure to reclaim them in the following decades is a safe point to assume most Roman citizens understood that the golden years were behind them.
The balkans were contested by nomads like the Avars and Bulgars, and the Anatolia was raided almost every year by the Arabs. The lost eastern provinces made up most of the wealth of the empire, and Egypt and the Levant were the main source of grain (food) for Constantinople. Everyone would notice the decline in prestige and wealth, and it would be hard to deny that the Romans were no longer the dominant force in the region.
When actually isn't the right question to ask, but where.
Also to determine at what point a formerly Roman citizen might have "figured out" that "civilization" (in quotes because of the impreciseness of definition) was over, presumes a harder question that can only be answered by us in hindsight. Namely, "are the Romans coming back?"
For this, the only universally acknowledged "where" would be Roman Britain, between 370-430. In the span of a single person's life, you would have someone who grew up with towns, villas, a complex economy integrated into the rest of the empire, to a massively localized "economy" and material culture, living in a landscape of abandoned villas, crumbling monumental structures, dying towns, and remilitarized hilltop forts. And more importantly, an understanding that the cause of such trauma was the departure of Roman administration. The change occurred quick enough for the remaining sub-Roman brits to remember that they used to be Roman, and to send a letter to Aetius requesting that the Romans come back.
As for elsewhere, this problem gets a little more dicey. Because when you're talking about "civilization collapse", your first presumption is to assume it as material economy collapse. But see, just because you have a regressed economy, does not mean you would view your cultural world as also collapsing.
The lower danube region suffered massive economic trauma and de-urbanization in the aftermath of the battle of Adrianople in 378 with rampaging Goths around the countryside. It was so bad that the archaeological reports say that literally every villa in the region was destroyed by fire, and classical cities as we and they understood them did not return until well into the high medieval era. And yet, there was no presumption amongst the denizens of that region of "Roman civilization collapsing," because the Romans were still there. They were just clustering in the new "urban" centers which were barely urban at all, and instead just heavily fortified administrative hubs. To apply a more modern analogy, just because Detroit and rust belt cities are dying, does that mean American civilization is dying? Some might argue yes, but most people would be aware that the state has in no ways left Detroit, that economic depression does not equate to a vaporization of one's cultural world. Also there are still other shining beacons of "civilization" elsewhere within the country, like New York City or LA.
In almost all of the other cases, the changeover from Roman to "barbarian" occurred so imperceptibly slowly, and usually with some degree of assent by the populace and elites, or alternately for people with living memory of Roman rule, were still aware of the possibility of the return of the Roman state (see for example, Justinian's reconquest of Africa, Italy, and Spain), that it would be hard for any of them to "figure anything out."
Interestingly, there's really only one other "where" that could be answered as to where/when Roman citizens felt their world was collapsing. Byzantine Anatolia, when the Arabs began their speedy conquests. Literally every city in the region was sacked 2-3 times over, military and economy was collapsing everywhere, there were signs that the Roman Empire was about to collapse and be taken over.
And yet, Byzantine Anatolia remained Roman for another solid 400 years. Coastal Anatolia another 300 after that.
So long story short, we as Americans all love a good apocalypse story. Partly because apocalypse to Americans is really a wish fulfillment fantasy, where we get to be the ones in charge of our destiny, not this all crushing state. But in reality, like the actual demise of an entire world, with very specific regional exceptions, the changeover was complex, and frequently imperceptible.
It was at the very least, not universally apocalyptic enough for most of the average citizens to believe something very wrong had happened, and the world would never be the same again.
In 90% of the case (because 90% of the late Roman world were agriculturalists), they just kept on farming. Something that would continue until well into the early modern era.
On a broader level, can the collapse of a civilization be experienced by individuals, or it's a lengthy process that overcome one's lifespan?
I would also add "can the collapse of a civilization only be identified in hindsight"?
Your average artisan living in Lutetia, say, might have known that the times were a' changing, but would he have been able to say "this is the collapse of my civilization" even when the Visigoths were battering down the gates?
I know that the Roman empire didn't dissolved overnight, but were there a certain period in which a Roman citizen could just say: well, everything changed around here, from now one, nothing will be the same again?
You're running into the issue with your question: It really depends on where "here" is. Where is your "common Roman citizen" and when? Is he or she a 5th century Romano-Britain or Carthaginian under the rule of a different people? A 6th century Constantinopolitan at the height of Justinian's conquests? A 7th century Egyptian who hasn't known imperial rule for decades?
There's no convenient point in history where the "whole Roman civilization" collapsed.