Well, you have to look at “The Plan” to see how that was possible. But first, to discuss manufacturing capability…
The Cylons being could manufacture themselves continuously, and just because we didn’t see massive construction shipyards in the series didn’t mean they weren’t there. Look at the typical WWII movie – unless the story focused on characters who’s job it is to deliver the equipment to war, the focus is usually on the soldiers themselves. The equipment is secondary and supports the story. Trying to “explain too much” is the death of drama: set up the premise, explain it, and detail just enough to inform the viewer as to what’s going on. Otherwise you’ll do stuff like, oh, explain how “Midiclorians” work…
Now, back to the “The Plan,” which was to infiltrate the defense grid and remotely disable all networked ships. Except for Galactica (and Pegasus) that plan worked. The Plan was also to catch the Colonies by surprise, and they did, so a lot of the ships probably were destroyed in shipyards or on the ground (as we heard of in the Razor story).
And finally, nuking the Colonies didn’t even require a lot of ships – just one Base Star per planet can sit in low orbit and lob nukes at will, as the planet revolved below it (and nukes are fairly “cheap” to make compared to ships). They could adjust their orbit to deliver a full spread to all major population centers within hours. And foot solders? You don’t need that many, and you can always “wait out” a population dying of radiation poisoning…
(A better question is how the Galactica could continue to get Vipers in the air. They didn’t have an unlimited supply, and they kept getting blown up. I think the show’s creative staff tried to explain that with the addition of the Pegasus and their fleet of Vipers that supplemented the ones Galactica had on board…)