I would think of it as annealing/gradient descent instead of some kind of Markov process where maybe you get lucky every 2-5 years. You are not breeding for the purpose of getting one animal with the trait (well you can, but not necessarily) so much as you are trying to influence a population of animals to display the traits you want over time. Maybe first generation you have an average yield of X across 100animals. And you don’t let the lowest yielding 50% breed (or just have them breed less so you can’t counteract inbreeding), now generation 2 has an average yield of 1.05X across 100animals. If you know the trait is heritable it seems pretty straightforward.

What’s challenging is I guess you can’t know a priori much about the actual genetics at play so at a certain point it becomes hard to know what’s simply phenotypic variance independent of genetics and what’s actually genes - it could take quite a while to be certain you’ve “converged”. Or for something more subjective/without an obvious strong genetic link, it could take a while to rule out the possibility of breeding for the trait at all.

Like for humans, I’m highly confident you could do some basic process over 10 generations to breed some ridiculously tall people. But it helps we know it has huge variance, is highly heritable, is easy to measure, and is polygenic. Probably a lot harder to try to breed “nice” people or people with thick skin. The fact dog breeders can do things like that is much more impressive IMO.