Step 1: Lay out the rejection timeline. Hyperacute is immediate, acute is days-to-weeks, and chronic is months-to-years; the prefix hyper signals the most rapid response.
Step 2: Hyperacute rejection is driven by pre-existing antibodies (typically from ABO incompatibility) that are ready to strike the moment blood flows into the graft, so the organ blanches and thromboses within minutes, often visible during surgery itself.
Step 3: Therefore 24 hours, 2 weeks, and years all describe slower categories and are incorrect for hyperacute rejection.
Step 4: The correct timing is within minutes.
\[\boxed{\text{Within minutes}}\]