You can set up a Form Action that will update a form's status automatically upon having submitting the completed form.

In order to add a Modify Form Status Action to your Form, go to Forms > View Form Templates > choose the edit arrow for the template you would like the action added to > Actions tab > + New Action. Then you can select Modify Form Status in the Action type dropdown.

Once you've set the Action up with the settings that you want to execute it, then you will have a form that can automatically update the status. You can add more than one Modify Form Status actions if you would like the form to go through various stages.