Unlike the others, I would not at all be inclined to discourage them, or wait over a year for zebras to mature. Zebras are sexually mature at three months. They live by a breed fast, die young strategy in the wild and there are ZERO further maturations to occur once they get their adult colors. There will be no changes in the birds after that time and if you want to breed them that young, if they're willing, they will be fine. I have bred finches at this age - or rather, the finches did it themselves in an aviary, and no issues whatsoever.
If you want to breed the finches, they are adults and they are old enough. Give them a nest and they will figure it out. Get them on a good diet of seeds, pellets, greens and hard boiled egg, provide eggshell and cuttlebone and you are unlikely to ever experience egg binding - I've raised hundreds of finches (plus tiels, budgies, and doves), and not dealt with it yet because my birds eat well and get exercise out of the cage (females kept in cages all the time and not bieng able to fly is a big factor in eggbinding, I suspect.)
Zebra finches are super easy to breed and usually they do everything just fine themselves. I have never had to interfere. But they can be aggressive. Be prepared to remove the chicks once they are weaned, or dad may attack them.
Zebras love a nest, and a nest provides enrichment to them to build it. You can keep one in the cage at all times, but they will breed frequently. If you don't want further chicks after the first clutch just pop little holes in the tops of the eggs with a pin. They will still sit for up to a month on each clutch, and so in the end the female don't lay that many eggs a year.
I am personally familiar with female zebra finches which have laid four to five eggs a month every month all year, and have still reach 10+ years of age. They are extremely well adapted to reproduce like mice, and with a good diet, it won't harm them. Most zebra hens will lay eggs no matter what, in food cups, water troughs, anything at all they can fit into, and if not just on the cage floor. I have a friend with zebra hens who would lay en egg every single night on the floor! She gave them nests, and they would then lay just a few and sit for a ong time - so with a nest they were laying much less. Other finches usually will not lay without a nest, or will only do so sporadically - my society hen and canary if I don't give them nests will drop a couple every few weeks through this time of year, and they usually break and get eaten. But zebras are a different animal and their determination to lay is remarkable.
