I have found DbC very handy for jumpstarting the red-green-refactor cycle because it helps in identifying unit tests to start with. With DbC I start thinking about pre-conditions that the object being TDD-ed must handle and each pre-condition might represent a failing unit test to start a red-green-refactor cycle. At some point I switch to start the cycle with a failing unit test for a post-condition, and then just keep the TDD flow going. I have tried this approach with newcomers to TDD and it really works in kickstarting the TDD mindset.
In summary, think of DbC as an effective way to identify key behavioral unit tests. DbC helps at analyzing inputs (pre-conditions) and outputs(post-conditions), which are the two things that we need to control (inputs) and observe (outputs) to write testable software (a similar aim of TDD).