In content-connected projects, you can automatically assign documents to a translator if a user with a proper language combination is available among the users in the project. In addition to the existing auto-assign modes, a third one is available: Put document up for FirstAccept.
After you created a content-connected project, go to Project home > Settings, and click the Content Connector icon. Navigate to the Connection section. Select the Put document up for FirstAccept option, and enter a deadline in the FirstAccept deadline text field.