Is Your Setting Viable?
#Is Your Setting Viable? YesYes. Actually, it looks like (modern) humans evolved before the last glacial period. The wiki article on humans say the first "modern" humans appeared around 200 000 years ago. The last glacial period was from 110 000 to 12 000 years ago. It looks like humans did evolve before the Ice Age!
Side Note
#Side Note EvolutionEvolution of the Human species is still happening. It happens when people mate, when people are born, and when people die. It happens when people value certain attributes over others. Evolution has happened and is happening as you read this very paragraph. The time scale, however, is very long. I wouldn't expect a new species of human to pop up tomorrow, or in the next 1000 years. In fact, the most recent estimate of the last human-chimp common ancestor was 5 to 6 million years ago.
That being said, we can see some differences in humans down the line from us. For instance, the ability to consume milk as an adult seems to be a recent evolutionary thing. In fact, it looks like the people who can do so are the mutants!