Ancient audiences were familiar with the Oedipus story. How does Sophocles create suspense, despite our knowing the end?

This is a good question, but your question assumes something that might not be true. Just because you know how a story ends, it does not mean that the story will have no suspense. Don't people read and watch the same movie several times? Here are few reasons why:

1. Everytime you watch something again, you tend to learn or see something new.

2. Also you have to keep in mind that you are not the same person when you watch something twice. For this reasons, there is a freshness to watching something for a second time.

3. Finally, there is a dramatic atmosphere that draws the audience in. This alone create suspense.