There are several misconceptions here.
The first is that scientific hypotheses are assessed not based on some ideal standard of perfect prediction, but in comparison to other possible hypotheses. The confirmation of the predictions are the facts.
Basically, evolutionary theory is successful at predictions. For example, one would predict that human populations who life at high altitudes would develop over time some way to cope with the lack of oxygen, and in fact a gene variant was discovered in Tibetans recently that does just that. One would also expect that populations that have been at high altitudes for a longer period of time would have had time to develop better coping mechanisms; in fact that has been discovered to be the case as the genetic mechanisms of Tibetans is more efficient than the increased hemoglobin production of indigenous peoples in the Andes, an area settled much more recently by humans. Any theory that would compete with evolutionary theory would need to predict these and thousands of other facts; the opponents of evolution have failed to come up with any such competing theory. The theory that humans and apes have a common ancestor also makes a number of predictions: Fossils of creatures intermediate in form, DNA similarities the magnitude of whose correlation should correspond to the fossil record, and susceptibility to similar diseases. Again, these predictions have been confirmed. These facts do not make humans any less special, it just shed light on how HaShem went about the process of creation.
The second misconception is that evolution is incompatible with Torah. Nothing could be further from the truth. Evolution is one way that HaShem allows His creatures to adapt to changing circumstances. Understanding the scientific processes HaShem has created gives us an even greater appreciation of His greatness.
Evolutionary theory is so important to modern biology that if you reject it, you really do have to reject all of modern biology. Fortunately, there is no need for a believing Jew to do this. Nor is there even a need to doubt the scriptures and midrash that describe a different sequence of creation. As Rashi notes in his comments to the very first verse in the entire Torah, the Torah was not given to us for the purpose of explaining the sequence. The Torah instead tells us how to live in HaShem’s amazing universe.