What are you talking about? Evolution happens at the level of populations not individuals. If it sounds like a stupid idea that a species would “evolve” a male and independently “evolve” a female and they would mate and “start” a new species, you’re right. Nobody claims that is how evolution works though. All offspring are always the same species as their parents. But if you divide a population and put part of the population in a different environment, isolated from the rest of the population, given enough time, the split off population will adapt to its new environment and a new species may emerge that is no longer reproductively compatible with the other descendants of the original population living in the original environment.
There are thousands of transitional fossils you can view in museums.