Thank you all for your replies!
It's comforting to know I could apply for a PhD before I officially get my Master's diploma (of course as you all stressed, it depends on the uni).
But I have to say I was surprised that the application process starts so early, some of the offers are already unavailable, I hope I will find something if I start looking for it, let's say, in a month.
Thank you all again!
Martyna