They don't have a "concept" of the first bird?
Correct.
Well they certainly have a "concept" of our supposed first ape like ancestor.
Incorrect. They have a concept of ancestral populations that became increasingly ape-like over time, but there was no first ape.
An analogy: who was the first person to speak French, and to whom did he speak it?
There has to be a first bird in evolution
why?
and there also has to be a bird-like ancestor before that and so on and so forth back to the first single celled organism in the pool of goo...if the random mutation is incremental.
The fact that mutation/selection/etc. is incremental is the reason why there is no first bird. The idea of a first bird is a creationist notion, not an evolutioary notion.
Or does some non-flying animal suddenly pop out wings and feathers, webbed feet, and the ability to make nests?
The animal you described would have been a first bird, which doesn't exist in evolutionary theory.