Except that we *do* find exactly such animals in the fossil record. We actually *do* see dinosaurs with feathers that were ancestors to modern birds. We *do* have fossils of teansitional forms between 'fish' and 'land crawlers'. For that matter, we have *modern* species that bridge that gap.
And yes, among the scientific community that studies these questions in detail, the support for evolution is universal.
First, evolution and the Big Bang have nothing to do with each other. One is biology, the other is cosmology. The evidence for the two is different and independent.
The Big Bang has been amply supported by the evidence from the cosmic background radiation, which has allowed the development of precision cosmology over the last decade or two.
Far from being under stress, the overall BB scenario is focusing more on details now that we have the evidence to test our previous questions.
You show one misconception: the universe did NOT 'appear out of nothing'. There was no time when there was 'nothing'. In other words, whenever there was time, there was matter, energy, and space.