Maiden milkers are relatively common in goats, especially ones from high-producing bloodlines. I think it's mostly down to luck though - if you happen to have a doe that shows any signs of bagging up and you're sure she's not pregnant, try massaging and milking out anything that's there to see if it encourages further milk production. I wouldn't rely on the method as a milk supply though.
If you google 'maiden milker' or 'pseudolactation' you'll probably find a few discussions about this.
I used to call this a precocious milker. I've never seen it in goats, but I've heard about it. As Burra pointed out, it happens primarily in heavy milk production bloodlines. It happens commonly in dogs if they "adopt" a kitten, puppy, or other animal that suckles on their nipples. Usually within a week or so, the dog is successfully nursing the adoptee. I've also heard about it in humans, but don't have any firsthand knowledge. I just recall my aunts and great aunts talking about some relative who successfully nursed an orphaned infant by letting the baby attempt to suckle frequently. It caused the woman to lactate.
Precocious millers goats don't produce as much milk as a normally lactating goat, nor for as long. No personal experience on this, but this is what I've read in the textbooks.
It's never too late to start! I retired to homestead on the slopes of Mauna Loa, an active volcano. I relate snippets of my endeavor on my blog : www.kaufarmer.blogspot.com