We didn't evolve from monkeys and apes, that's a misconception. We had "common ancestors", beings that diversified and grew into different species. We can see animals changing now, with elephants with no tusks surviving poachers. more are now being born without any as an example.
Apes (including humans) and monkeys had common ancestors that lived about 30 million years ago. That ancestor didn't magically turn into monkeys and apes, the would have been small differences that sent different subsets of the population in different directions. Sometimes the difference is advantageous and begins to be represented more often.
To use this example on the elephants, it is likely in the future elephants without tusks will start outnumbering elephants with tusks. It could be the start of a new species happening right before our eyes. It is these little differences happening over millions of years that make the seemingly impossible changes we observe now.
Our closest relative is the chimpanzee. This does not mean we evolved from chimpanzees. It would have been a small change happened to the animal that came before us that sent us into different directions, such as potentially spending more time on the ground than amongst trees. Natural genetic variations that were advantageous to this new lifestyle would come to dominate the group spending more time on the ground, while the group still living in the trees would slowly develop traits that favour that lifestyle.
So when we split off, we were very similar. You probably would not have been able to tell them apart. It's taken 13 million years for us to look as different as we do now, and even then we look pretty similar!