It took 600 years from the decline of the Roman Empire to the rise of the Renaissance. So 600 years is the meterstick for this kind of thing, though Rome didn't collapse in two hours like the world did in Fallout.
But I highly doubt the world will ever be "Normal" again. For starters, the whole point of the Resource Wars that lead into the Final War was battling over Earth's few remaining fossil fuel resources. There's literally not enough left to restart Civilization as it had been.
Yeah, let's ignore the Eastern Roman (Byzantine) Empire, the Carolingian Empire, the Abbasid Caliphate and so on. They might not have had the relative power of Rome in its heyday (which didn't have it for that long either) but they all achieved things the Romans didn't and certainly made their territory relatively safe and prosperous.
By the way there's more than 600 years between the Fall of Rome and the Italian Renaissance, unless you meant the Carolingian Renaissance of course, but that one was less than 600 years.
Actually civilization is restarting retardedly slow in the Fallout Universe circa FO3/NV, we might not expect cities, reliable long distance travel and so on. But it doesn't even show villages being built new, everyone lives literally in the garbage of a past civilization. How about chopping some trees for houses? Painting your shacks? Plastering the outsides of them? Cleaning up the damn skeletons everywhere? That's basic stuff for which you don't need advanced technology, ffs, they've been doing it for millennia.
I know they're going for some frontier feel, but they've done a [censored] job of explaining it. Suspension of disbelief only goes so far.
But IIRC NCR/Shady Sands is a pretty clean city now, the slides at the end of FO2 at least showed it pristine. Likewise we can probably assume all of NCR is pretty much living in clean actually functioning villages/towns.
Still love the game though if I'm sounding a bit too negative.