One may begin to fast even in a state of ritual impurity

At times Messenger of Allah ﷺ used to get up in the morning in the state of Janaba after having sexual relations with his wives. He would then take a bath and fast.  

أَنَّ رَسُولَ اللَّهِ ﷺ كَانَ يُدْرِكُهُ الْفَجْرُ وَهُوَ جُنُبٌ مِنْ أَهْلِهِ ثُمَّ يَغْتَسِلُ وَيَصُومُ