The Cursed Child is garbage, and cannot be canon regardless of what Joanne says, because it breaks the mechanics of time travel established in Prisoner of Azkaban. The book (and the film) establishes that time travel via time turner can’t change the past, because by the time you use the time turner, the “changes” you set out to make have already been made. This is evidenced by the fact that it was Harry who saved his past self and Sirius from the dementors. And in fact all of the trio’s actions in the past are actually foreshadowed in the book (and in the film) before they go back and perform them.
But even if you don’t accept that, it’s also impossible to go back in time nearly that long by time turner. Prisoner of Azkaban establishes that each turn of the time turner takes you back one hour (Dumbledkre recommends that three turns ought to do it, and they go back three hours). To go back in time a single year would take 8,760 turns. Assuming one turn per second, that’s just under about 2 and a half hours. To go back 13 years would take about 32 and a half hours of nonstop turning. Even if you grant that they could do that, they would be physically exhausted from sleep deprivation, badly dehydrated, and probably very hungry when they arrived.
