Highly unlikely. In order for only one species of mammal to develop, you would need to somehow prevent any speciation to have occurred during the entire development path from fish to human. To do this, you’re going to have to keep the entire population very small and prevent them from ever splitting into multiple reproductively isolated groups. I don’t think that’s even possible on an earth-like planet, you’re inevitably going to get a situation where a successful species has spread enough for multiple reproductively isolated populations to occur. Even if your pre-human mammal species is limited to a tiny island with no chance to become physically isolated, you still have the chance of isolation via different populations on that island becoming adapted for different ecological niches. Consider, for example, the finches of the Galapagos - started out from one initial population and proceeded to differentiate into multiple species adapted for different food sources.
Secondly, even if you did somehow prevent any speciation during the evolutionary period, I doubt you’d end up with something like a human. Evolution is driven by competition and change. An isolated population in an unchanging environment and no opportunity to diversify into multiple competing populations is going to reach a form optimized for the local environment, and then not change.
I think the only way you could get a world with humans and no other complex animals would be with outside intervention, some deliberate force weeding out side branches and only permitting development towards modern humans. A sure sign of Intelligent Design, or alien manipulation or something.