There are already intelligent species other than humans, except they don't have the physical abilities to do a lot of the things humans can. Some birds, pigs, dogs, rats, and of course apes are very intelligent. I don't see why it would be impossible, over billions of years humans evolved to be what they are now, of course a new branch of species could evolve eventually
There are already millions of species of intelligent organisms other than humans.
Even if you take your case for the sake of argument to say that there were not, well of course it could happen again at any time. The fact that humans exist is in itself, evidence for that.
I think that in many years there is a good chance of a race to evolve next to humans, but they may not evolve along a natural path due to human intervention. We would study them profusely, and as a result, our technology would alter their evolutionary path. If it happened, we would have to keep our interaction to a minimum.
Humanity has committed genocide on its kind for being too different from themselves. We can barely handle someone being of a different race let alone a different species. We may reach a point where we could coexist with another intelligent species but not now. If you disagree then ask a neanderthal how evolving alongside us worked out.