They didn't. The Chixculub crater is so huge that its shape can't be understood from the ground, and it's old enough that that shape is most visible with modern remote sensing technology- the surface features are submerged or eroded. The impact is dated to 66 million years ago; for comparison, that's before India joined the Eurasian continent and formed the Himalayas. Figure 1(b) of this article shows the elevation map of the Yucatan Peninsula, and there's not much to see.

The crater was first recognized in 1981. While doing aeromagnetic scanning on an oil survey, Glen Penfield and Antonio Camargo identified a pattern of magnetic and gravitational anomalies forming concentric circles over 200 kilometers across. These were caused by disruptions in ancient geologic strata and changes in crust thickness; Penfield and Camargo interpreted this as either volcanic activity or an impact event. In 1991, Alan Hildebrand combined their efforts with new geologic core samples and published a paper both confirming Chicxulub as a crater and associating it with the extinction at the end of the Cretaceous.