Question: I am currently finishing my masters in Germany and I will start my PhD soon. I will be having a TV-L contract, however, I haven't acquired my official diploma yet. In case that the bureaucratic stuff are not finished before my starting day, would I still be able to sign the contract by proving I have submitted my thesis (or getting something like 4,0 bescheinigung)? Or do I have to wait until I am officially graduated?

Answer: 
There is no general answer I guess. I know how my university handles this (in Bavaria): If you have no official diploma yet, you will be employed within TV-L 12. Once you provide the diploma, you will be "upgraded" to TV-L 13. A 4,0-Bescheinigung is not sufficient.

I'm sure you can find out quickly by calling someone from HR.
To sign a TV-L 13 contract, you definitly need a proof that you have a master's degree (or something equivalent). I think a 4.0-Bescheinigung should suffice but this might also depend on your university's policies for that matter. As pointed out already, go check with your university's HR department.