One thing to remember is that Darwin didn't come up with the theory of evolution. Darwin came up with a mechanism to explain evolution, natural selection. The idea of evolution existed long before Darwin. in Darwin's day evolution went by the name of Lamarckism, named after the guy who came up with it, Lamarck. His version of evolution had organisms acquire traits during their lifetime which they then passed on and lost traits that they didn't use.

There's a scene in Lucretius' On the Nature of Things (Latin philosophical poem of the first century BCE, Loeb translation quoted below) that gives an insight into his view (although I'm not aware of how common this view was):

whatever you see feeding on the breath of life, either cunning or courage or at least quickness must have guarded and kept that kind from its earliest existence; many again still exist, entrusted to our protection, which remain commended to us because of their usefulness.

Firstly, the fierce brood of lions, that savage tribe, has been protected by courage, the fox by cunning, by swiftness the stag. But the intelligent dog, so light of sleep and so true of heart, and all the various kinds which are sprung from the seed of beasts of burden, woolly sheep also, and horned breeds of oxen, all these have been entrusted to men's protection, Memmius. For these have eagerly fled from the wild beasts, they have sought peace and the generous provision gained by no labour of theirs, which we give them as the reward of their usefulness.

So, Lucretius proposes that all species have always existed in their current form (and that many other species once existed, but became extinct due to their inability to survive and reproduce). Animals which were unable to survive on their own (like domesticated animals) either became extinct or were useful to humans and therefore taken under human protection.

EDIT: typo