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We want the prophecy and the hilltop scene to be as close together in time as they can be, I think, because the gap between them is time Voldemort sat on the prophecy apparently doing nothing, and the longer that is, the less believable.
I don't think he 'did nothing'. First he had to wait for the boys to be born to see which one of them actually was born in late July (rather than in early July or early August). But even after that, he waited because he was plotting to use the momentum from the killing of the prophecy boy to take over the entire Wizarding Britain within less than a year - ie he needed a man at Hogwarts (Severus) and access to major players at the Ministry (Barty Jr). Which means he wasn't going to move on Harry before September 1981 in any case.
I don't think he 'did nothing'. First he had to wait for the boys to be born to see which one of them actually was born in late July (rather than in early July or early August). But even after that, he waited because he was plotting to use the momentum from the killing of the prophecy boy to take over the entire Wizarding Britain within less than a year - ie he needed a man at Hogwarts (Severus) and access to major players at the Ministry (Barty Jr). Which means he wasn't going to move on Harry before September 1981 in any case.