All the time entries on a new project have a non-billable status by default. Why so?
This can happen if you have set the project's Contract Type to Marketing or Overhead. By default, Core marks all time entries of the projects of these contract types as non-billable. If this is the case, you should update the contract type of the project in order to bill time on that. Core prompts you to mark the existing entries on such a project as billable when you do so. Check out the Core Help for details on various contract types.