Anaximander lost out to Aristotle in the running for Most Famous Ancient Greek Philosopher. That's a shame, as he may have been the first person to come up with the idea of "animals evolving from other animals." The only problem is, the spin on it he came up with involved post-puberty humans hatching from fish people.
Darwin's era was not the first time that people began wondering where humans come from. Throughout history the debate is one, and the side arguing against pure creationism (though not necessarily against theism) has been stymied by the old "chicken and egg" question. You can't get an adult without raising it from a baby, and you can't get a baby without an adult. How to get out of that cycle?
One of the first to come up with a fact-based solution to this was Anaximander – a Greek philosopher born around 610 BC. Granted, it was the wrong solution, but what could he do? It took a lot of background research to come up with the theory of evolution by natural selection, and he lived roughly 2,500 years before any of it happened.
Anaximander believed in a progression of animal forms, and that "humans were born from other kinds of animals." He went too literal with his interpretation of "born," but to be fair to him, he did so because he followed the evidence. Anaximander was observational, and one of the things he observed was fetal development. At a time when people still lived in close contact with the animals they ate, this wasn't so unusual. He had the ability to look at fetal, or still-developing, mammals, birds, and fish. It also appears that he had some experience looking at human fetuses in early stages of development. To Anaximander, the earliest stage of fetal development, in any animal, looked like an early developing fish. If something gestated long enough, he reasoned, it could grow into all kinds of things.
He solved the "which came first, the human or the baby" problem this way. Everything began in the ocean. Some fish-creatures allowed their young to develop over a long time – long enough that the fetuses went through puberty and were able to take care of themselves. The fish creatures came to shore and beached themselves. The humans inside of them split them open, and walked out onto dry land, ready to make actual babies and take care of them.
Okay, so it's not perfect. But I've heard worse guesses.