Shivneri bus to mumbai?

I want to go to mumbai tomorrow or day after. The earlier I reach my destination in the morning, the better. I looked for buses on the MSRTC website. The first one I found from wakad bridge was 6:58 AM (reaches dadar at 10) and next was 7:58 am and so on. I believe there are buses that reach dadar from pune much earlier than 10 am for sure. Does it mean that each and every bus before 6:58 AM is filled already? Is it preferable to book on the spot instead? Please help me out.