Alzheimer's disease (AD) is now defined based on its underlying brain pathology, with the presence of amyloid (Aβ) plaques at high enough levels sufficient to warrant a diagnosis in the absence of cognitive symptoms. High levels of PET-detectable Aβ are widely thought to be the first imaging marker, with structural brain changes detectable on MRI scans thought to occur later. We combined 4570 longitudinal MRIs and 1684 Aβ PET scans from three cognitively healthy cohorts to test the difference in cortical thickness and its change between those that subsequently converted to be Aβ-positive or stayed Aβ-negative, using MRIs acquired exclusively in the years before conversion. We found those that subsequently developed elevated Aβ levels show both thicker cortex and less cortical thinning, even when the last MRI used to estimate their thickness trajectories was acquired at least seven years before conversion. Many effects remained when accounting for quantitative Aβ levels, suggesting some cortical thickness effects may be partly independent of Aβ. Differences in cortical thickness and its change between converters and Aβ-negative individuals showed moderate alignment with patterns of Aβ deposition, and the timing of thickness changes tracked the temporal progression of Aβ accumulation. Thus, if amyloid is AD, we show that high levels of PET-detectable amyloid are not the first imaging marker of AD, as cortical thickness changes can be traced years before pathological amyloid. This has implications for understanding the sequence of events leading up to the earliest stages of AD.