I have never owned finches personally, but, in my opinion, as long as they are in the same cage together, this will be a constant battle (because they will become stimulated and mate etc).
If eggs are laid, it is not as straightforward of a process as many would assume...It can lead to all sorts of issues and parents are sometimes terrible to their babies.
Suggestion A: get smaller food bowls or feed them on some sort of platform (?)--If you do use a platform, make sure it is high enough up not to cast a shadow (or they will just try to nest under it). Also, make sure food doesn't appear to be too plentiful. Times of excess increase the likelihood of your birds deciding that "now" would be a good time to raise a family. Avoid super fatty foods and squishy/warm foods as well (as these can also contribute). Oh--and make sure they don't have any of those grass-type shred toys, as they are showing hormonal behaviors already..These CAN be okay, but not in hormonal situations. Just because you do this, does not mean you will not have to deal with the egg issue, but it might discourage them slightly....Keep in mind: If they mate and an egg is on the way, it is going to come out somewhere--if it lands on the floor, then that's fine (as your intent is not to breed).
Suggestion B: Make sure they have access to cuddle-bone because if she is trying to lay an egg, she will need the nutrients therein to pass it etc. Keep a close eye on her behavior and if you see her straining, eating less or looking "pregnant" it could be a sign of egg-binding and she will need veterinary attention ASAP.
Suggestion C: If eggs show up, they will usually lay more than one over a short-ish span of time (in parrots, it can be take a few days for the whole clutch to show up)---If you allow the eggs to mature, then you will be faced with more birds and inbreeding issues (birds will mate with their siblings in captivity, and inbreeding can lead to health issues). Consequently, unless you have the setup to give each baby its own cage eventually, you probably shouldn't go this route. There are some sad ways of dealing with unwanted fertile eggs...You can't just take them away or the bird will immediately be stimulated to mate/lay again. You must leave them in the cage until the bird loses interest and decided they aren't hatching. Consequently, you have to make it so that the eggs don't hatch (even if sat upon) without removing them from the cage for more than a few minutes. You can A) replace them with dummy eggs (which may be hard to find...AND may or may not be convincing) OR, the alternative is to boil the eggs (like a hard-boiled egg) and return them to the cage as soon as they are cool enough to go back in safely. I know that sounds terrible, but that is what a lot of people do...
Babies are quite complicated and the parents can sometimes do some pretty nasty things (like kill them or reject them)....So nature makes it look pretty straightforward, but that's just because we don't see all of the nastiness that happens in reality....
Suggestion D: Make sure they are getting enough sleep and that they are getting it on a schedule. Too little sleep can lead to hormonal issues as well.
How much are they getting nightly?
Suggestion E: Separate them if you can (or if you want, try all of the other suggestions first and if they don't help, do this as a last resort)...The thing is, this will likely never stop being an issue when you have a male and female together. It can even be an issue when 2 birds of the same gender are together (minus the babies, but with the risk of egg-laying). Laying eggs is risky and laying fertile eggs is even more complicated...so....that is why I say to separate. You will never be totally out of the woods as long as they are living in the same cage. If you separate them, you could put them right next to each other (although they may become frustrated).... The proximity of the other bird is going to impact hormones, but the mating is definitely going to produce the strongest effect (which is why a barrier is important if breeding is an issue).
Final thought--- just because you haven't seen them "do the deed", does NOT mean that they haven't. It doesn't take long and unless you watch them 24/7 without ever using the bathroom etc, then you could easily miss it.
