Dating the creed to within a few years of the crucifixion is an apologist’s inference. All we actually know is that Paul wrote 1 Corinthians in the 50s.

The exact window is inferred from Paul’s travels, not read off a dated document, and it is fair to say so. But the inference is not special pleading. Paul says he received tradition, that he visited Peter and James in Jerusalem about three years after his conversion, and that his gospel matched what the Jerusalem apostles preached. With a conversion around AD 33 to 36, that places the tradition in the mid 30s, which is why skeptical scholars such as Lüdemann and James Crossley date its core to within a few years of the events. Even a generous margin of a decade leaves no room for a legend to grow.