There’s a big difference between a “bipedal” species and a “hominid” species. Are you asking whether any primates stand a chance of evolving into a species that is self-aware on the level that humans are? It’s not impossible, but I think it’s far more likely that we will push them to extinction through habitat loss before there is time for that to happen.
We don’t currently have a way to effectively model the formation of new species in the way that you mean. We can predict the discovery of new species, and we can artificially select for new species having traits we choose, but we can’t predict how species will evolve, since we can’t know what genetic mutations will occur, or how (or how quickly) genes will be acted on by a species’ environment, especially since the environment itself also changes in ways we can’t predict.
I will also add that evolution does not have to be a slow process. Every time the frequency of an allele changes in a population, that is evolution. Speciation, however, is usually a slow process – unless the organisms have a very short lifetime, as in bacteria or some insects.