THE TIME TURNER IS A PART OF THE BIG PLAN!
(This theory gels in with some of the stuff in SCB: Percy had a Time-Turner. So this is going to be slightly lengthy. Stay with me)
Because, when it came to protecting Harry, the Time Turner was Dumbledore’s safety net!
When Sirius broke out of Azkaban, Dumbledore would’ve guessed he would try to break into Hogwarts, even more so because Sirius kept saying, “he’s at Hogwarts!”, in his cell. Sirius was extremely talented (since childhood) and having broken OUT of a Dementor-protected prison, Dumbledore would’ve gathered that he could also break IN to a dementor-protected school and possibly break through other any extra defences put up at Hogwarts. Dumbledore NEEDED to PROTECT Harry at all costs. And this is where the TIME TURNER comes in. The Time Turner is potentially a means for Dumbledore to go back in time and save Harry, should Sirius manage to (or it would seem so in the beginning) kill Harry.
Here are the supporting arguments: