Every step where the altered child can no longer breed with the parent species is an insurmountable hurdle, since it’s an evolutionary dead-end..."
Surely you know that's not how it works, don't you?
For sake of discussion, let's consider a hypothetical example -- critter-X, beginning population 1,000, reproduces every year.
Critter-X is perfectly adapted to its environment, but over geological time the environment changes.
As the climate grows colder, baby-X's born with longer hair & stubbier legs survive better, so over time, the entire population gets more winterized.
Now the environment grows hotter & dryer, new predators arrive and only Critter-X's built for more speed survive.
In time the climate grows very wet and now Critter-X's who swim do better.
Adaptions to new environments can happen slowly, resulting in occasional population collapses, down to just a few breeding individuals.
Then populations explode when adaptions better match environment.
Multiply these changes times millions and at the end of that time there's no way the offspring could still interbreed with their ancestral population.
And yet at no time during this was any offspring ever born in a different species from its parents.
Sure, some "baby-steps" are more rapid than others, but none is ever a giant leap forward.
That's evolution theory, which our deniers claim is contradicted by fossil records.
The fossils show "sudden appearance" and then "stasis", they say.
But it's important to notice that still 99%+ of species have not been found.
And we do have one rather important sequence of fossils transition forms: