[Ph.D. without substantive previous Pol.Sci. experience]

It's fairly common for people from different backgrounds to do PhDs in Political Science, I don't think you should worry too much about this. Try to make it clear on your SoP that you're familiar with the field and know what you're getting yourself into. It's probably also helpful if some of your recommenders are political scientists and if your writing sample is directly related to what you want to study.