Cursed Child spoilers!
I don’t think Delphi was acting on her own. Too many things happen at the right times for everything to be either coincidence or the work of just one girl. In any case, others were definitely at least aware of her existence; she was raised by the Rowles, a Death Eater family, and clearly brought up believing that her mission in life was to bring back her father, or at least, to continue his legacy. Who’s to say that others with Death Eater connections didn’t know about her, as well, and didn’t play a part in hiding her, or even help with her time turner plot? There certainly seems to be a resurgence in Death Eater and dark creature activity, according to Hermione:
“There are mountain trolls riding Graphorns through Hungary, there are giants with winged tattoos on their backs walking through the Greek Seas, and the werewolves have gone entirely underground … These are people and beasts that fought alongside Voldemort in the great wizarding wars. These are allies of darkness. This – combined with what we have just unearthed at Theodore Nott’s – could mean something” (24-25, Nook edition).
I object to werewolves being described as “allies of darkness” and offer you Remus Lupin as a counterexample, but regardless, there’s something going here. The giants with winged tattoos seem especially relevant, most likely an Augurey reference, since Delphi has a similar tattoo herself. And Theodore Nott, a former classmate of Harry’s from a Death Eater family, was arrested in possession of the very same time turner Delphi manipulates Albus and Scorpius into using. Is it possible he let himself be caught? It’s hard to imagine anyone would go to Azkaban willingly, but if he knew the time turner was going to be used to change the past so that Voldemort won, he just might have agreed to it. That would explain how Delphi knew the Ministry had a time turner, and certainly makes more sense than Theodore Nott holding onto a prototype of a device he’d made for someone else and long since finished.
The improved version went to none other than Lucius Malfoy. Now, when Draco comes forward with the time turner, he assures Harry that his father didn’t intend to use it to bring Voldemort back. But would he have admitted to anything else? And would he have even known what his father’s plans were? He clearly didn’t know about Delphi, but I find it hard to believe his parents didn’t, especially since she would be their niece and was probably born in their house. The part about secretly preferring to live in a world without Voldemort is something I can believe of Draco, but not his father. And since it’s implied that Lucius Malfoy is dead (he is only referred to in past tense), who can say what the time turner’s original purpose was? You don’t go to the trouble to procure a rare, dangerous, illegal device if you’re not planning to use it.
What makes more sense? A chain of coincidences, all somehow relating to Death Eaters, their families, and the dark creatures that fought on Voldemort’s side? Or a scheme that’s been planned out, perhaps for years, by those who remain of Voldemort’s supporters?