Actually, the main rebuilding aspect would be increasing their population size - everything else is pretty much already there (the technology, cities, etc.).
There was only about 5500 aliens left.
They seemed to have been technologically developed species to implement automation (whatever they had) and use it to aid in rebuilding. They also appeared to have been on possibly late 20th century level before getting anti-matter technology from Earth (Which provided a significant boost).
They didn't bomb themselves into the dark ages, retained technology and most (if not all) of their knowledge and even had anti-matter weapons by the time Voyager showed up (so, they learned quite a few tricks - which shows they are similarly adaptive species).
With a major problem gone (their poisonous atmosphere), they pretty much have it easy from that point on on the road to recovery if the society is cohesive enough for that (it seemed to have been), and I suspect that Janeway may have also provided them with some better anti-matter radiation containment technology as well to protect from potential future leakages (unless they developed this themselves at some point before Voyager arrived).
With no more failed child births due to radiation sickness, etc., I suspect their population would start increasing quite rapidly.
But we also don't know how fast it takes them to carry kids to term, mature, maybe have limits on how many kids they have, couplings, etc.
If they eschew monogamy for a time (assuming they had and implemented this concept to begin with) while already being a technologically developed species, population growth could easily explode.
They have a much larger genetic baseline than the human colonists from 'Up the long ladder', so if we assume similar intervention to increase population (possibly even using artificial means to speed things up even more), how much could their population increase in say 35 years?
If they are anything like Humans, and assuming 2% population growth, you're looking at a doubling of their population in 35 years.
Higher population growth = more births over same period of time (which would depend on how many kids each couple decided to have.
If we assume 3% population growth (same as sub-Saharan Africa) per 100 years, you end up with 105 702 people.
In 200 years (assuming same population growth is maintained), their population would increase to over 2 million (only looking at natural births - no technological intervention).
Its possible UFP and Starfleet had trained to educate alien cultures or survivors on how to bring themselves back up to viable numbers (population-wise) in the shortest time frame possible.
From Wikipedia:
At the turn of the 20th Century, the Hutterite community of North America – which is, incidentally, highly inbred – achieved the highest levels of population growth ever recorded, doubling every 17 years. It’s a tough ask, but if each woman had eight children, we’d be back to seven billion people and our current population crisis in just 556 years.
The aliens in our Trek scenario have a much larger population startup (5500) with viable genetic baselines and therefore far lower chances of birth defects and overall problems down the line.
If each woman had about 4 children instead (half as much as the BBC posits for the Hutterites), then in 102 years, the population would increase to 176 000.
It would take them 153 years of that reproductive growth to reach 1.4 million (with no technological intervention).
